Recent questions in Limits and Derivatives

For some constants $a$ and $b$ , find the derivative of $(ax^2+b)^2$

asked Apr 9, 2014 by thanvigandhi_1

1 answer

For some constants $a$ and $b$ , find the derivative of $(x-a)(x-b)$

asked Apr 9, 2014 by thanvigandhi_1

1 answer

Find the derivatives of $x^n+ax^{n-1}+a^2x^{n-2}+...+a^{n-1}x+a^n$ for some fixed real number $a$

asked Apr 9, 2014 by thanvigandhi_1

1 answer

For the function $f(x) = \large\frac{x^{100}}{100}$ $+ \large\frac{x^{99}}{99}$ $+...+\large\frac{x^2}{2}$ $+x+1$ then $f'(1)$ is

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Find the derivative of the given function from first principle $\Large\frac{x+1}{x-1}$

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Find the derivative of the given function from first principle $\Large\frac{1}{x^2}$ .

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Find the derivative of the given function from first principle $(x-1)(x-2)$

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Find the derivative of the given function from first principle $x^3-27$

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Find the derivative of $x$ at $x = 1$ .

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Find the derivative of $99x$ at $x = 100$ .

asked Apr 7, 2014 by thanvigandhi_1

1 answer

Find the derivative of $x^2-2$ at $x = 10$

asked Apr 7, 2014 by thanvigandhi_1

1 answer

$f(x)=\left\{\begin{array}{1 1}mx^2+m,&x<0\\nx+m,&0 \leq x \leq 1 \\nx^3+m,&x>1 \end{array}\right.$ 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