Balbharati solutions for Mathematics and Statistics 1 (Commerce) [English] 11 Standard Maharashtra State Board chapter 7 - Limits [Latest edition]

Evaluate the following limit:

${\displaystyle \underset{x\to 3}{lim}\left[\frac{\sqrt{x+6}}{x}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 2}{lim}\left[\frac{x^{-3}-2^{-3}}{x-2}\right]}$

Evaluate the following limit:

${\displaystyle \underset{x\to 5}{lim}\left[\frac{x^3-125}{x^5-3125}\right]}$

Evaluate the following limits: if ${\displaystyle \underset{x\to 1}{lim}\left[\frac{x^4-1}{x-1}\right]=\underset{x\to \text{a}}{lim}\left[\frac{x^3-{\text{a}}^3}{x-\text{a}}\right]}$, find all the value of a.

Evaluate the following limit:

${\displaystyle \underset{x\to 7}{lim}\left[\frac{(\sqrt[3]{x}-\sqrt[3]{7})(\sqrt[3]{x}+\sqrt[3]{7})}{x-7}\right]}$

Evaluate the following limits: if ${\displaystyle \underset{x\to 5}{lim}\left[\frac{x^{\text{k}}-5^{\text{k}}}{x-5}\right]}$ = 500, find all possible values of k.

Evaluate the following limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{{(1-x)}^8-1}{{(1-x)}^2-1}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{\sqrt[3]{1+x}-\sqrt{1+x}}{x}\right]}$

Evaluate the following limits: ${\displaystyle \underset{y\to 1}{lim}\left[\frac{2y-2}{\sqrt[3]{7+y}-2}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to \text{a}}{lim}\left[\frac{{(z+2)}^{\frac{3}{2}}-{(\text{a}+2)}^{\frac{3}{2}}}{z-\text{a}}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 5}{lim}\left[\frac{x^3-125}{x^2-25}\right]}$

Evaluate the following limits: ${\displaystyle \underset{z\to 2}{lim}\left[\frac{z^2-5z+6}{z^2-4}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to -3}{lim}\left[\frac{x+3}{x^2+4x+3}\right]}$ 

Evaluate the following limits: ${\displaystyle \underset{y\to 0}{lim}\left[\frac{5y^3+8y^2}{3y^4-16y^2}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to -2}{lim}\left[\frac{-2x-4}{x^3+2x^2}\right]}$

Evaluate the following limits: ${\displaystyle \underset{u\to 1}{lim}\left[\frac{u^4-1}{u^3-1}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 3}{lim}[\frac{1}{x-3}-\frac{9x}{x^3-27}]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 2}{lim}\left[\frac{x^3-4x^2+4x}{x^2-1}\right]}$

Evaluate the following limit:

${\displaystyle \underset{x\to -2}{lim}\left[\frac{x^7+x^5+160}{x^3+8}\right]}$

Evaluate the following limits: ${\displaystyle \underset{y\to \frac{1}{2}}{lim}\left[\frac{1-8y^3}{y-4y^3}\right]}$

Evaluate the following limits: ${\displaystyle \underset{\text{v}\to \sqrt{2}}{lim}\left[\frac{{\text{v}}^2+\text{v}\sqrt{2}-4}{{\text{v}}^2-3\text{v}\sqrt{2}+4}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 3}{lim}\left[\frac{x^2+2x-15}{x^2-5x+6}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{\sqrt{6+x+x^2}-\sqrt{6}}{x}\right]}$

Evaluate the following limits: ${\displaystyle \underset{y\to 0}{lim}\left[\frac{\sqrt{1-y^2}-\sqrt{1+y^2}}{y^2}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 2}{lim}\left[\frac{\sqrt{2+x}-\sqrt{6-x}}{\sqrt{x}-\sqrt{2}}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to \text{a}}{lim}\left[\frac{\sqrt{\text{a}+2x}-\sqrt{3x}}{\sqrt{3\text{a}+x}-2\sqrt{x}}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 2}{lim}\left[\frac{x^2-4}{\sqrt{x+2}-\sqrt{3x-2}}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 1}{lim}\left[\frac{x^2+x\sqrt{x}-2}{x-1}\right]}$

Evaluate the following limits:  ${\displaystyle \underset{x\to 0}{lim}\left[\frac{\sqrt{1+x^2}-\sqrt{1+x}}{\sqrt{1+x^3}-\sqrt{1+x}}\right]}$

${\displaystyle }$Evaluate the following limits: ${\displaystyle \underset{x\to 4}{lim}\left[\frac{x^2+x-20}{\sqrt{3x+4}-4}\right]}$

Evaluate the following limits: ${\displaystyle \underset{x\to 2}{lim}\left[\frac{x^3-8}{\sqrt{x+2}-\sqrt{3x-2}}\right]}$

Evaluate the following limits: ${\displaystyle \underset{y\to 2}{lim}\left[\frac{2-y}{\sqrt{3-y}-1}\right]}$

Evaluate the following limits: ${\displaystyle \underset{z\to 4}{lim}\left[\frac{3-\sqrt{5+z}}{1-\sqrt{5-z}}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{9^x-5^x}{4^x-1}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{5^x+3^x-2^x-1}{x}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{\log (2+x)-\log (2-x)}{x}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{3^x+3^{-x}-2}{x^2}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}{\left[\frac{3+x}{3-x}\right]}^{\frac{1}{x}}}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{\log (3-x)-\log (3+x)}{x}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{{\text{a}}^{3x}-{\text{b}}^{2x}}{\log 1+4x}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{{(2^x-1)}^2}{(3^x-1)\times \log (1+x)}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{{15}^x-5^x-3^x+1}{x^2}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 2}{lim}\left[\frac{3^{\frac{x}{2}}-3}{3^x-9}\right]}$

Evaluate the following:

${\displaystyle \underset{x\to 0}{lim}\left[\frac{{\left(25\right)}^x-2{\left(5\right)}^x+1}{x^2}\right]}$

Evaluate the following: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{{\left(49\right)}^x-2{\left(35\right)}^x+{\left(25\right)}^x}{x^2}\right]}$

if ${\displaystyle \underset{x\to 2}{lim}\frac{x^{\text{n}}-2^{\text{n}}}{x-2}}$ = 80 then find the value of n.

Evaluate the following Limits: ${\displaystyle \underset{x\to \text{a}}{lim}\frac{{(x+2)}^{\frac{5}{3}}-{(\text{a}+2)}^{\frac{5}{3}}}{x-\text{a}}}$

Evaluate the following Limit:

${\displaystyle \underset{x\to 0}{lim}\frac{{(1+x)}^{\text{n}}-1}{x}}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 2}{lim}\left[\frac{(x-2)}{2x^2-7x+6}\right]}$

Evaluate the following limit:

${\displaystyle \underset{x\to 1}{lim}\left[\frac{x^3-1}{x^2+5x-6}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 3}{lim}\left[\frac{x-3}{\sqrt{x-2}-\sqrt{4-x}}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 4}{lim}\left[\frac{3-\sqrt{5+x}}{1-\sqrt{5-x}}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{5^x-1}{x}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}{(1+\frac{x}{5})}^{\frac{1}{x}}}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{\log (1+9x)}{x}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\frac{{(1-x)}^5-1}{{(1-x)}^3-1}}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{{\text{a}}^x+{\text{b}}^x+{\text{c}}^x-3}{x}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\frac{{\text{e}}^x+e^{-x}-2}{x^2}}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{x(6^x-3^x)}{(2^x-1)\cdot \log (1+x)}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{{\text{a}}^{3x}-{\text{a}}^{2x}-{\text{a}}^x +1}{x^2}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{{(5^x-1)}^2}{x\cdot \log (1+x)}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{{\text{a}}^{4x}-1}{{\text{b}}^{2x}-1}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{\log 100+\log (0.01+x)}{x}\right]}$

Evaluate the following Limits: ${\displaystyle \underset{x\to 0}{lim}\left[\frac{\log (4-x)-\log (4+x)}{x}\right]}$

Evaluate the limit of the function if exist at x = 1 where, f(x) = ${\displaystyle \{\begin{array}{ll}7-4x& x<1\\ x^2+2& x\ge 1\end{array}}$