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Recent questions tagged ch6
Questions
Find the equation of the normals to the curve $y = x^3 + 2x + 6$ which are parallel to the line $x + 14y + 4 = 0$.
cbse
class12
bookproblem
ch6
sec3
q21
p213
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equation of the normal at the point \((am^2,am^3)\) for the curve \(ay^2 = x^3.\)
cbse
class12
bookproblem
ch6
sec3
q20
p212
sec-b
easy
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the points on the curve \(x^2 + y^2 - 2x - 3 = 0\) at which the tangents are parallel to the \(x\) - axis.
cbse
class12
bookproblem
ch6
sec3
q19
p212
sec-b
easy
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
For the curve $y = 4x^3 – 2x^5$, find all the points at which the tangent passes through the origin.
cbse
class12
bookproblem
ch6
sec3
q18
p212
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the points on the curve $y = x^3$ at which the slope of the tangent is equal to the $y$ - coordinate of the point.
cbse
class12
bookproblem
ch6
sec3
q17
p212
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Show that the tangents to the curve \(y = 7x^3 + 11\) at the points where \(x = 2\) and \(x = -2\) are parallel.
cbse
class12
bookproblem
ch6
sec3
q16
p212
sec-a
easy
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equation of the tangent line to the curve $y = x^2 - 2x +7$ which is $(a)$ parallel to the line $2x - y + 9 = 0$
cbse
class12
bookproblem
ch6
sec3
q15
q15-a
p212
sec-b
easy
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equations of the tangent and normal to the given curves at the indicated points: $ y = x^4 - 6x^3 + 13x^2 - 10x + 5\; at \;(0, 5)$
cbse
class12
bookproblem
ch6
sec3
q14
q14-1
p212
sec-b
easy
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find points on the curve $ \large\frac{x^2}{9} + \frac{y^2}{16} = 1$ at which the tangents are $(i)\; parallel\; to\; x - axis$
cbse
class12
bookproblem
ch6
sec3
q13
q13-1
p212
sec-b
easy
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Find the equation of all lines having slope $0$ that are tangents to the curve $ y=\large \frac{1}{x^2-2x+3}$
cbse
class12
bookproblem
ch6
sec3
q12
p212
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the equation of all lines having slope \(2\) that are tangents to the curve $ y= \large\frac{1}{x-3}, $$\: x \neq 3$
cbse
class12
bookproblem
ch6
sec3
q11
p212
sec-a
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the equation of all lines having slope $–1$ that are tangents to the curve $ y= \large\frac{1}{x-1}, $$ \: x \neq 1$
cbse
class12
bookproblem
ch6
sec3
q10
p212
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the point on the curve $y = x^3 - 11x + 5$ at which the tangent is $y = x -11$.
cbse
class12
bookproblem
ch6
sec3
q9
p212
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find a point on the curve $y = (x – 2)^2 $ at which the tangent is parallel to the chord joining the points $(2, 0)$ and $(4, 4)$.
cbse
class12
bookproblem
ch6
sec3
q8
p211
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find points at which the tangent to the curve $y = x^3 - 3x^2 - 9x + 7$ is parallel to the $x$ - axis.
cbse
class12
bookproblem
ch6
sec3
q7
p211
sec-a
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the normal to the curve $ x = 1 - a \sin\theta, y = b \cos^2\theta$ at $ \theta = \Large {\frac{\pi}{2}}$
cbse
class12
bookproblem
ch6
sec3
q6
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the normal to the curve $ x = a \cos^3\theta, \: y = a \sin^3\theta$ at $ \theta =\Large {\frac{\pi}{4}}$.
cbse
class12
bookproblem
ch6
sec3
q5
p211
sec-b
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the tangent to the curve $y = x^3 - 3x + 2$ at the point whose $x$ - coordinate is $3$.
cbse
class12
bookproblem
ch6
sec3
q4
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the tangent to curve $ y = x^3 - x + 1$ at the point whose $x$ - coordinate is $2$.
cbse
class12
bookproblem
ch6
sec3
q3
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the tangent to the curve $\normalsize y =\large { \frac{x-1}{x-2},} \normalsize x \neq 2\; at\;x = 10$
cbse
class12
bookproblem
ch6
sec3
q2
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the tangent to the curve $y = 3x^4 – 4x \; at\; x = 4.$
cbse
class12
bookproblem
ch6
sec3
q1
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
The interval in which $y = x^2 e ^{- x}$ is increasing is
cbse
class12
bookproblem
ch6
sec2
q19
p206
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function given by \(f (x) = x^3 – 3x^2 + 3x - 100\) is increasing in \(R.\)
cbse
class12
bookproblem
ch6
sec2
q18
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function \(f\) given by $f (x) = \log \cos\: x$ is strictly decreasing on $ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly increasing on, $\left( \large {\frac{\pi}{2},} \normalsize \pi\right)$
cbse
class12
bookproblem
ch6
sec2
q17
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function $f$ given by $f (x) = \log \sin x$ is strictly increasing on$ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly decreasing on $\left( \large {\frac{\pi}{2}}, \pi\right)$
cbse
class12
bookproblem
ch6
sec2
q16
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Let $I$ be any interval disjoint from $[–1, 1]$. Prove that the function $f$ given by \( f(x) = x + \frac{1}{\large x}\) is strictly increasing on $I$.
cbse
class12
bookproblem
ch6
sec2
q15
p206
sec-b
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the least value of a such that the function $f$ given by $f (x) = x^2 + ax + 1$ is strictly increasing on $(1, 2).$
cbse
class12
bookproblem
ch6
sec2
q14
p206
sec-b
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
On which of the following intervals is the function $f $ given by $f (x) = x^{100} + sin x –1$ strictly decreasing ?
cbse
class12
bookproblem
ch6
sec2
q13
p206
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Which of the following functions are strictly decreasing on $\left(0, \: \large {\frac{\pi}{2}}\right)$
cbse
class12
bookproblem
ch6
sec2
q12
p206
sec-b
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function \(f\) given by \(f (x) = x^2 – x + 1\) is neither strictly increasing nor strictly decreasing on \((– 1, 1).\)
cbse
class12
bookproblem
ch6
sec2
q11
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the logarithmic function is strictly increasing on $(0, \infty).$
cbse
class12
bookproblem
ch6
sec2
q10
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that \( y =\large { \frac{4\sin\theta}{(2+\cos\theta)}}-\normalsize \theta\) is an increasing function of \(\theta\) in $\left[0, \: \large {\frac{\pi}{2}}\right]$
cbse
class12
bookproblem
ch6
sec2
q9
p205
sec-b
easy
modelpaper
2012
q15
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the values of $x$ for which $y = [x(x – 2)]^2$ is an increasing function.
cbse
class12
bookproblem
ch6
sec2
q8
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that $ y = log(1+x)-\large {\frac{2x}{2+x}}, \normalsize x > – \normalsize 1$, is an increasing function of $x$ throughout its domain.
cbse
class12
bookproblem
ch6
sec2
q7
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the following functions are strictly increasing or decreasing: $(a) \;x^2 + 2x - 5$
cbse
class12
bookproblem
ch6
sec2
q6
q6-a
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the function f given by $f (x) = 2x^3 – 3x^2 – 36 x + 7$ is (a) strictly increasing and (b) strictly decreasing ?
cbse
class12
bookproblem
ch6
sec2
q5
p205
sec-b
easy
modelpaper
2012
q16
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the function $f$ given by $f (x) = 2x^2 - 3x$ is $(a) $ strictly increasing
cbse
class12
bookproblem
ch6
sec2
q4
q4-b
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by $f (x) = \sin x$ is neither increasing nor decreasing in $(0, \pi)$
cbse
class12
bookproblem
ch6
sec2
q3c
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by $f (x) = \sin x$ is strictly decreasing in $(\large {\frac{\pi}{2}},$$ \pi)$
cbse
class12
bookproblem
ch6
sec2
q3
q3b
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by \(f (x) = \sin \;x\) is strictly increasing in $\left(0, \: \large {\frac{\pi}{2}}\right)$
cbse
class12
bookproblem
ch6
sec2
q3
q3a
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by $f(x) = e^{2x}$ is strictly increasing on $R$.
cbse
class12
bookproblem
ch6
sec2
q2
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by \(f (x) = 3x + 17\) is strictly increasing on \(R\).
cbse
class12
bookproblem
ch6
sec2
q1
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the total revenue in Rupees received from the sale of $x$ units of a product is given by $Rx = 3x^2 +36x + 5$. The marginal revenue, when $x = 15$ is
cbse
class12
bookproblem
ch6
sec1
q18
p199
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ cm is
cbse
class12
bookproblem
ch6
sec1
q17
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
The total revenue in Rupees received from the sale of $x$ units of a product is given by $ R(x) = 13x^2 + 26x + 15.$ Find the marginal revenue when $x = 7$.
cbse
class12
bookproblem
ch6
sec1
q16
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $ C(x) = 0.007x^3 - 0.003x^2 + 15x + 4000.$ Find the marginal cost when 17 units are produced.
cbse
class12
bookproblem
ch6
sec1
q15
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Sand is pouring from a pipe at the rate of $12 cm^3/s$. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
cbse
class12
bookproblem
ch6
sec1
q14
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
A balloon, which always remains spherical, has a variable diameter $\large\frac{3}{2}$$(2x+1)$. Find the rate of change of its volume with respect to $x.$
cbse
class12
bookproblem
ch6
sec1
q13
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
The radius of an air bubble is increasing at the rate of $ \large\frac{1}{2}$ cm/s. At what rate is the volume of the bubble increasing when the radius is $1\; cm$?
cbse
class12
bookproblem
ch6
sec1
q12
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
A particle moves along the curve $ 6y = x^3 +2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.
cbse
class12
bookproblem
ch6
sec1
q11
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
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