Limits and Derivatives

Class 11 NCERT

NCERT

1   Evaluate the Given limit:$\lim \limits_{x \to 3}x+3$

Solution :

$\lim \limits_{x \to 3}x+3=3+3=6$

2   Evaluate the Given limit:$\lim \limits_{x \to \pi} (x-\dfrac{22}{7})$

Solution :

$\lim \limits_{x \to \pi}(x-\dfrac{22}{7})=(\pi-\dfrac{22}{7})$

3   Evaluate the Given limit:$\lim \limits_{r \to 1}\pi r^2$

Solution :

$\lim \limits_{r \to 1} \pi r^2=\pi(1^2)=\pi$

4   Evaluate the Given limit: $ \lim \limits_{x \to 1}\dfrac{4x+3}{x-2}$

Solution :

$\lim \limits_{x \to 1} \dfrac{4x+3}{x-2}=\dfrac{4(1)+3}{1-2}=\dfrac{4+3}{-1}=-7$

5   Evaluate the Given limit: $ \lim \limits_{x \to -1}\dfrac{x^{10}+x^5+1}{x-1}$

Solution :

$\lim \limits_{x \to -1}\dfrac{x^{10}+x^5+1}{x-1}\\ =\dfrac{(-1)^{10}+(-1)^5+1}{-1-1}\\ =\dfrac{1-1+1}{-2}=-\dfrac{1}{2}$