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Recent questions tagged ch13
Questions
If $\lim\limits_{x\to \infty}\big(\large\frac{x^3+1}{x^2+1}$$-(ax+b)\big)=2$ then
jeemain
math
ch13
limits and derivatives
introduction to limits
easy
q82
asked
Dec 30, 2013
by
sreemathi.v
1
answer
$\lim\limits_{h\to 0}\large\frac{f(2h+2+h^2)-f(2)}{f(h-h^2+1)-f(1)}$ given that $f'(2)=6$ and $f'(1)=4$
jeemain
math
class11
ch13
limits-and-derivatives
differentiability
easy
q80
asked
Dec 30, 2013
by
sreemathi.v
1
answer
Let $f:R\to R$ be such that $f(1)=3$ and $f'(1)=6$.Then $\lim\limits_{x\to 0}\bigg[\large\frac{f(1+x)}{f(1)}\bigg]^{1/x}$ equals
jeemain
math
class11
ch13
limits-and-derivatives
differentiability
easy
q79
asked
Dec 30, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}\large\frac{\sin(\pi\cos^2x)}{x^2}$=
jeemain
math
ch13
limits-continuity-and-differentiability
limits-of-trigonometric-functions
easy
q78
asked
Dec 30, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 1}\large\frac{\sqrt{1-\cos 2(x-1)}}{x-1}$=
jeemain
math
ch13
limits-continuity-and-differentiability
differentiability
easy
q77
asked
Dec 30, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to \infty}\large\frac{x^n}{e^x}$$=0$ for
jeemain
math
ch13
limits-continuity-and-differentiability
introduction to limits
easy
q75
asked
Dec 30, 2013
by
sreemathi.v
1
answer
If $G(x)=-\sqrt{25-x^2}$ then $\lim\limits_{x\to 1}\large\frac{G(x)-G(1)}{x-1}$ is
jeemain
math
ch13
limits-continuity-and-differentiability
introduction to limits
easy
q74
asked
Dec 30, 2013
by
sreemathi.v
1
answer
$\lim\limits_{\theta \to \Large\frac{\pi}{2}}(\sec\theta-\tan\theta)$=
jeemain
math
class11
ch13
limits-and-derivativeslimits of trigonometric functions
easy
q73
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}\large\frac{\tan x-\sin x}{x^3}$=
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q72
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to \infty}[x-\sqrt{x^2+x}]$=
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q71
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to a}\large\frac{\log(x-a)}{\log(e^x-e^a)}$ is
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q68
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to\Large\frac{\pi}{6}}\large\frac{3\sin x-\sqrt 3\cos x}{6x-\pi}$ equals
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q67
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}\large\frac{\cos(\sin x)-1}{x^2}$=
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q66
asked
Dec 24, 2013
by
sreemathi.v
1
answer
If $f(x)=\left\{\begin{array}{1 1}\large\frac{\sin[x]}{[x]}&[x]\neq 0\\0&[x]=0\end{array}\right.$ then
jeemain
math
class11
ch13
limits and derivatives
limits-of-trigonometric-functions
easy
q64
asked
Dec 24, 2013
by
sreemathi.v
1
answer
If $\lim\limits_{x\to 0}\large\frac{\sin px}{\tan 3x}$$=4$ then value of p is
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q62
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to \infty}\large\frac{(2x-3)(3x-4)}{(4x-5)(5x-6)}$=
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limts
easy
q61
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\sqrt 2\cos x-1}{\cot x-1}$=
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q59
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}\large\frac{(1-\cos 2x)\sin 5x}{x^2\sin 3x}$=
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q56
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}\large\frac{\sin x-x}{x^3}$=
jeemain
math
class11
ch13
limits-and-derivatives
limits of trigonometric funtions
easy
q55
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to \large\frac{\pi}{4}}\large\frac{\sqrt 2\cos x-1}{\cos x-1}$=
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q53
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}(1+ax)^{\Large\frac{b}{x}}$=
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q52
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 1}\bigg[\large\frac{x^3+2x^2+x+1}{x^2+2x+3}\bigg]^{\Large\frac{1-\cos(x-1)}{(x-1)^2}}$
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q51
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 2}\large\frac{2^x+2^{3-x}-6}{\sqrt{2^{-x}-2^{1-x}}}$ is
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q49
asked
Dec 24, 2013
by
sreemathi.v
1
answer
Value of $\lim_{x\to 2^-}\{x+(x-[x]^2)\}$ is
jeemain
math
class11
ch13
continuity-and-differentiability
differentiability
easy
q46
asked
Dec 24, 2013
by
sreemathi.v
1
answer
$\lim\limits_{n\to\infty}\large\frac{n^p\sin^2(n!)}{n+1}$$\qquad0 < p < 1$ is equal to
jeemain
math
ch13
limits-continuity-and-differentiability
introduction to limits
easy
q45
asked
Dec 24, 2013
by
sreemathi.v
1
answer
If $\lim\limits_{x\to 0}(1+ax)^{\Large\frac{b}{x}}=e^2\qquad(a,b\in N)$ then
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q44
asked
Dec 23, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 1}\large\frac{x^3+x^2-2}{\sin(x-1)}$ is
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q42
asked
Dec 23, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}\big(\large\frac{a^x+b^x+c^x}{3}\big)^{\Large\frac{1}{x}}$ is
jeemain
math
class11
ch13
limits-and-derivatives
introduction of limits
easy
q41
asked
Dec 23, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}\large\frac{(\cos x)^{1/2}-(\cos x)^{1/3}}{\sin^2x}$ is
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q40
asked
Dec 23, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to \infty}\big(\large\frac{x+1}{x+2}\big)^{2x+1}$ is
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q39
asked
Dec 23, 2013
by
sreemathi.v
1
answer
If $f(x)=\mid x-25\mid$ and $g(x)=f(f(x))$,find $g'(x)$ for $x > 50$
jeemain
math
class11
ch13
limits-and-derivatives
differentiability
easy
q36
asked
Dec 23, 2013
by
sreemathi.v
1
answer
Evaluate :$\lim\limits_{x\to 0}(\cos x)^{\large\frac{1}{x^2}}$
jeemain
math
class11
ch13
limits-and-derivatives
limits of trigonometric functiond
easy
q35
asked
Dec 23, 2013
by
sreemathi.v
1
answer
Evaluate :$\lim\limits_{x\to \Large\frac{\pi}{4}}\large\frac{\sqrt 2-\cos x-\sin x}{(4x-\pi)^2}$
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q34
asked
Dec 23, 2013
by
sreemathi.v
1
answer
Evaluate : $\lim\limits_{x\to\large\frac{\pi}{2}}\large\frac{\sin(\cos x)\cos x}{\sin x-cosec x}$
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q33
asked
Dec 23, 2013
by
sreemathi.v
1
answer
Evaluate : $\lim\limits_{x\to 0}\large\frac{e^x-e^{x\cos x}}{x+\sin x}$
jeemain
math
class11
ch13
limits-and- derivatives
limits-of-trigonometric-functions
easy
q32
asked
Dec 23, 2013
by
sreemathi.v
1
answer
Evaluate : $\lim\limits_{x\to 0}(1+\sin x)^{\Large\frac{1}{x^2}}$
jeemain
math
class11
ch13
limits and derivatives
introduction to limits
easy
q31
asked
Dec 23, 2013
by
sreemathi.v
1
answer
Evaluate : $\lim\limits_{h\to 0}\large\frac{(a+h)^2\sin(a+h)-a^2\sin a}{h}$
jeemain
math
class11
ch13
limits and derivatives
derivatives
easy
q30
asked
Dec 23, 2013
by
sreemathi.v
1
answer
If $\lim\limits_{x\to 0}\large\frac{\log(3+x)-\log(3-x)}{x}$$=K$ the value of $K$ is
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q23
asked
Dec 23, 2013
by
sreemathi.v
1
answer
$\lim\limits_{n\to\infty}\large\frac{1+2^4+3^4+......n^4}{n^5}$ - $\lim\limits_{n\to\infty}\large\frac{1+2^3+3^3+......n^3}{n^5}$ =
jeemain
math
classs12
ch13
integrals
definite integrals as limits of sum
easy
q22
asked
Dec 23, 2013
by
sreemathi.v
1
answer
If $f(x+y)=f(x).f(y) \forall x,y$ and $f(5)=2,f'(0)=3$ then $f'(5)$ is
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q21
asked
Dec 23, 2013
by
sreemathi.v
1
answer
If $f(1)=1,f'(1)=2$ then $\lim\limits\large\frac{\sqrt{f(x)-1}}{\sqrt x-1}$ is
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q20
asked
Dec 23, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}\large\frac{\log x^n-[x]}{[x]}$ $n\in N$ ($x$ denotes greatest integer less than or equal to $x$)
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q19
asked
Dec 23, 2013
by
sreemathi.v
1
answer
Let $f(x)=4$ and $f'(x)=4$. Then $\lim\limits_{x\to 2}\large\frac{xf(2)-2f(x)}{x-2}$ is given by
jeemain
math
class11
ch13
limits-and-derivatives
introduction to limits
easy
q17
asked
Dec 20, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to 0}\large\frac{\sin(\pi\cos^2x)}{x^2}$ equals
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q13
asked
Dec 20, 2013
by
sreemathi.v
1
answer
For $x\in R\lim\limits_{x\to \infty}\big(\large\frac{x-3}{x+2}\big)^x$=
jeemain
math
class11
ch13
limits-and-
derivatives
introduction-to-limits
easy
q12
asked
Dec 20, 2013
by
sreemathi.v
1
answer
If $G(x)=-\sqrt{25-x^2}$ then $\lim\limits_{x \to 1}\large\frac{G(x)-G(1)}{x-1}$ has the value
jeemain
math
class11
ch13
limits-and-derivatives
introduction-to-limits
easy
q11
asked
Dec 20, 2013
by
sreemathi.v
1
answer
If $f(x)=\sqrt{\large\frac{x-\sin x}{x+\cos^2x}}$ then $\lim\limits_{x\to \infty}f(x)$ is
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q9
asked
Dec 20, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to \infty}\big(\large\frac{x+6}{x+1}\big)^{x+4}$=
jeemain
math
class11
ch13
limits-and-derivatives
introduction-to-limits
easy
q7
asked
Dec 20, 2013
by
sreemathi.v
1
answer
If $f(9)=9,f'(9)=4$ then $\lim\limits_{x\to 9}\large\frac{\sqrt{f(x)}-3}{\sqrt x-3}$ equals
jeemain
math
class11
ch13
limits-and-derivatives
introduction-to-limits
easy
q6
asked
Dec 20, 2013
by
sreemathi.v
1
answer
$\lim\limits_{x\to -\infty}\bigg[\large\frac{x^4\sin(1/x)+x^2}{(1+|x|^3)}\bigg]$=
jeemain
math
class11
ch13
limits-and-derivatives
limits-of-trigonometric-functions
easy
q5
asked
Dec 20, 2013
by
sreemathi.v
1
answer
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