Recent questions tagged introduction to limits

Evaluate $\lim \limits_{x \to 2} \bigg( \large\frac{e^x-e^2}{x-2} \bigg)$

asked Apr 22, 2014 by meena.p

1 answer

Define $f(0)$ so that $f(x)=(x+1)^{\cot x}$ becomes continuous at $x=0$

asked Apr 22, 2014 by meena.p

1 answer

The function $f(x)=\large\frac{|x|}{x^2+2x}\qquad$$ x\neq 0$ and $f(0)=0$ is not continuous at $x=0$ because

asked Mar 26, 2014 by balaji

1 answer

If $\alpha,\beta$ are roots of $ax^2+bx+c=0$ then $\lim\limits_{x\to \alpha}\large\frac{1-\cos(ax^2+bx+c)}{(x-\alpha)^2}$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to a}\bigg($ $\bigg[$ $\big(\large\frac{a^{1/2}+x^{1/2}}{a^{1/4}-x^{1/4}}\big)^{-1}$ $-$ $\frac{2(ax)^{1/4}}{x^{3/4}-a^{1/4}x^{1/2}+a^{1/2}x^{1/4}-a^{3/4}}\bigg]^{-1}$ $-$ $(\sqrt 2)^{\large\log_4 a}\bigg)^8$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{x(1+a\cos x)-b\sin x}{x^3}$$=1$ then $a,b$ are

asked Jan 6, 2014 by sreemathi.v

1 answer

If $\lim\limits_{x\to \infty}\big(1+\large\frac{a}{x}+\frac{b}{x^2}\big)^{2x}$$=e^2$ then the value of a and b are

asked Jan 6, 2014 by sreemathi.v

1 answer

If $\lim\limits_{x\to a}\large\frac{a^x-x^a}{x^x-a^a}$$=-1$ and $a > 0$ then $a$=?

asked Jan 6, 2014 by sreemathi.v

1 answer

If $\alpha$ is a repeated root of $ax^2+bx+c=0$, then $\lim\limits_{x\to \alpha}\large\frac{\sin(ax^2+bx+c)}{(x-\alpha)^2}$ =

asked Jan 6, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\bigg[\large\frac{1^x+2^x+3^x+.........n^x}{n}\bigg]^{\Large\frac{1}{x}}$ is

asked Jan 6, 2014 by sreemathi.v

1 answer

Evaluate $\lim\limits_{\large x\to a}\large\frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt x}$, where $a\neq 0$

asked Jan 4, 2014 by sreemathi.v

1 answer

$ABC$ is an isosceles triangle inscribed in a circle of radius r. If $AB=AC$ and $h$ is the altitude from $A$ to $BC$, then the triangle $ABC$ has perimeter $P=2(\sqrt{2hr-h^2})+\sqrt{2hr})$ and area $A$=_______also $\lim\limits_{h\to 0}\large\frac{A}{p^3}=$_______

asked Jan 3, 2014 by sreemathi.v

1 answer

If $\lim\limits_{x\to \infty}\bigg[\large\frac{x^2+x+1}{x+1}$$-ax-b\bigg]=4$ then

asked Jan 3, 2014 by sreemathi.v

1 answer

$\lim\limits_{n\to \infty}\left\{\large\frac{1}{1-n^2} + \frac{1}{1-n^2} +......+ \large\frac{n}{1-n^2}\right\}$ is equal to

asked Jan 3, 2014 by sreemathi.v

1 answer

The function $f(x)=\large\frac{ln(1+ax)-ln(1-bx)}{x}$ is not defined at $x=0$. The value which should be assigned to $f$ at $x=0$ so that it is continuous at $x=0$ is

asked Jan 3, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 1}(\log_22x)^{\large\log_x5}$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

If $a,b,c,d$ are positive then $\lim\limits_{x\to \infty}\big(1+\large\frac{1}{a+bx}\big)^{c+dx}=$

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\big(\large\frac{x^2+5x+3}{x^2+x+2}\big)^x$ =

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{2^x-1}{\sqrt{1+x}-1}$=

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\large\frac{(1+x)^{1/x}-e}{x}$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

$\lim\limits_{x\to 0^+}x^m(\log x)^n,(m,n\in N)$ is

asked Jan 2, 2014 by sreemathi.v

1 answer

Use the formula $\lim\limits_{x\to 0}\large\frac{a^x-1}{x}=$$ln\; a$ to find $\lim\limits_{x\to 0}\large\frac{2^x-1}{(1+x)^{1/2}-1}$

asked Dec 31, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \infty}\big[\large\frac{x^2+5x+3}{x^2+x+3}\big]^x$

asked Dec 31, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\bigg[\large\frac{1+5x^2}{1+3x^2}\bigg]^{\Large\frac{1}{x^2}}$

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to a}\large\frac{\log(x-a)}{\log(e^x-e^a)}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}\big(\large\frac{a^x+b^x+c^x}{3}\big)^{1/x}$ is

asked Dec 30, 2013 by sreemathi.v

1 answer

If $\lim\limits_{x\to k}\large\frac{x^k-5^k}{x-5}$$=500$ then positive value of k is

asked Dec 30, 2013 by sreemathi.v

1 answer

If $x_1=1$ and $x_{n+1}=\large\frac{4+3x_n}{3+2x_n}\qquad$$n \geq 1$ and if $\lim\limits_{n\to \infty}x_n=l$ then l is

asked Dec 30, 2013 by sreemathi.v

1 answer

If $\lim\limits_{x\to \infty}\big(\large\frac{x^3+1}{x^2+1}$$-(ax+b)\big)=2$ then

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \infty}\large\frac{x^n}{e^x}$$=0$ for

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

asked Dec 30, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to \infty}[x-\sqrt{x^2+x}]$=

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

asked Dec 24, 2013 by sreemathi.v

1 answer

$\lim\limits_{x\to 0}(1+ax)^{\Large\frac{b}{x}}$=

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

asked Dec 24, 2013 by sreemathi.v

1 answer