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Recent questions tagged limits

$f(x)=\left\{\begin{array}{1 1}mx^2+m,&x<0\\nx+m,&0 \leq x \leq 1 \\nx^3+m,&x>1 \end{array}\right.$ \[\] For what integers $m$ and $n$ does $ \lim\limits_{x \to 0} f(x)$ and $ \lim\limits_{x \to 1} f(x)$ exist?

asked Apr 7, 2014 by thanvigandhi_1

1 answer

If the function $f(x)$ satisfies $ \lim\limits_{x \to 1} \large\frac{f(x)-2}{x^2-1}= \pi$ , evaluate $ \lim\limits_{x \to 1} f(x)$

asked Apr 7, 2014 by thanvigandhi_1

1 answer

$f(x)=\left\{\begin{array}{1 1}|x|+1,&x<0\\0,&x=0 \\|x|-1,&x>0\end{array}\right.$ \[\] For what value(s) of a does $ \lim\limits_{x \to a}f(x)$ exists?

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Let $a_1, a_2, ....,a_n$ be fixed real numbers and define a function $f(x) = (x-a_1)(x-a_2)...(x-a_n)$ \[\] What is $ \lim\limits_{x \to a_1}f(x)$? For some $ a \neq a_1, a_2,...,a_n$. Compute $ \lim\limits_{x \to a}f(x)$.

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Suppose $f(x)=\left\{\begin{array}{1 1}a+bx,&x<1\\4,&x=1 \\b-ax,&x>1\end{array}\right.$ and if $ \lim\limits_{x \to 1} f(x) = f(1) $ what are possible values of $a$ and $b$?

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Find $ \lim\limits_{x \to 5}f(x)$ where, $ f(x) = |x|-5$

asked Apr 5, 2014 by thanvigandhi_1

1 answer

Evaluate $\lim\limits_{x \to 0} f(x)$ where $f(x)=\left\{\begin{array}{1 1}\large\frac{x}{|x|},&x\neq 0\\0,&x=0\end{array}\right.$

asked Apr 5, 2014 by thanvigandhi_1

1 answer

Evaluate $\lim\limits_{x \to 0} f(x)$ where $f(x)=\left\{\begin{array}{1 1}\large\frac{|x|}{x},&x\neq 0\\0,&x=0\end{array}\right.$

asked Apr 5, 2014 by thanvigandhi_1

1 answer

Find $ \lim\limits_{ x \to 1} f(x)$, where $f(x)=\left\{\begin{array}{1 1}x^2-1, &x \leq 1\\-x^2-1, &x>1\end{array}\right.$

asked Apr 5, 2014 by thanvigandhi_1

1 answer

Find $ \lim\limits_{x \to 0} f(x) $ and $ \lim\limits_{x \to 1} f(x) $ where $f(x)=\left\{\begin{array}{1 1}2x+3, &x \leq 0\\ 3(x+1),& x > o\end{array}\right.$

asked Apr 5, 2014 by thanvigandhi_1

1 answer

Evaluate the given limit $ \lim\limits_{x \to \large\frac{\pi}{2}} \large\frac{\tan \: 2x}{ x - \Large\frac{\pi}{2}}$

asked Apr 5, 2014 by thanvigandhi_1

1 answer

Evaluate the given limit $ \lim\limits_{ x \to 0} ( \text{cosec} \: x - \cot\: x)$

asked Apr 5, 2014 by thanvigandhi_1

1 answer

Evaluate the given limit $ \lim\limits_{x \to 0} \large\frac{ \sin \: ax+bx}{ax+ \sin \: bx}$$a,b, a+b \neq0$

asked Apr 5, 2014 by thanvigandhi_1

1 answer

Evaluate the given limit $ \lim\limits_{x \to 0} x\sec x$

asked Apr 4, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{ x \to 0} \large\frac{ ax + x\cos\: x}{b\sin \: x}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{ x \to 0} \large\frac{\cos\: 2x-1}{\cos\: x - 1}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{x \to 0} \large\frac{ \cos \: x}{ \pi - x}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{ x \to \pi} \large\frac{ \sin ( \pi - x)}{ \pi ( \pi - x)}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits \[\] $ \lim\limits_{ x \to 0} \large\frac{ \sin \: ax}{ \sin \: bx}, $$ a , b \neq 0$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits: $ \lim\limits_{x \to 0} \large\frac{ \sin \: ax}{bx}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits: $ \lim\limits_{x \to -2} \Large\frac{ \Large\frac{1}{x}+ \Large\frac{1}{2}}{ \normalsize x +2}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{x \to 1} \large\frac{ax^2+bx+c}{cx^2+bx+a},$$ a+b+c \neq 0$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{\large z \to 1} \large\frac{\large z^{\large\frac{1}{3}}-1}{z^{\large\frac{1}{6}}-1}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{x \to 0} \large\frac{ax+b}{cx+1}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{x \to 3} \large\frac{x^4-81}{2x^2-5x-3}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{x \to 2} \large\frac{3x^2-x-10}{x^2-4}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{x \to 0} \large\frac{(x+1)^5-1}{x}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{ x \to -1} \large\frac{x^{10}+x^5+1}{x-1}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{x \to 4} \large\frac{4x+3}{x-2}$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{x \to 1} \pi r^2$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $\lim\limits_{x \to \pi} \bigg( x - \large\frac{22}{7} \bigg)$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

Evaluate the following limits $ \lim\limits_{x \to 3} x+3$

asked Apr 3, 2014 by thanvigandhi_1

1 answer

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