Question Paper of Calculus

Question 1:

$S i m p l i f y \sqrt{m^{3}} \times m^{2} \times \sqrt{m}$

Question 2:

$D i f f e r e n t i a t e y = \tan 3 x$

Question 3:

$D i f f e r e n t i a t e y = x^{2} e^{x}$

Question 4:

$F i n d t h e v a l u e o f \sum_{k = 0}^{5} (k^{2} + 1) . I f α a n d β a r e t h e r o o t s o f t h e e q u a t i o n 2 x^{2} — 6 x — 3 = 0, f i n d t h e v a l u e o f i) 2 α β i i) {(α + β)}^{2} i i i) \frac{1}{α} + \frac{1}{β} i v) α^{2} + β^{2}$

$T h e s e c o n d t e r m o f a g e o m e t r i c s e r i e s \frac{3}{8} a n d t h e s e v e n t h t e r m i s 12 . F i n d t h e 14 * t e r m .$

Question 5:

$F i n d a p r i m i t i v e f u n c t i o n o f : \frac{(1)}{{(2 +)}^{3}} \frac{x^{2}}{x^{3} + 2}$

Question 6:

$E v a l u a t e \lim_{x \to 2} \frac{x^{2} - 4}{x - 2}$

Question 7:

$E x p r e s s \frac{4}{\sqrt{5} + 2} w i t h a r a t i o n a l d e n o m i n a t o r ?$

Question 8:

$I f y = e^{x} i s a s o l u t i o n o f t h e e q u a t i o n \frac{d^{2} y}{d x^{2}} - 9 \frac{d y}{d x} + 14 y = 0 F i n d t h e v a l u e (s) o f k .$

Question 9:

$D i f f e r e n t i a t e y = \log_{e} (2 x + 1)$

Question 10:

$G i v e n t h e f u n c t i o n f (x) = x \sqrt{4 - x^{2}} S h o w t h a t y (x) i s a n o d d f u n c t i o n . F i n d t h e x a n d y i n t e r c e p t s o f t h i s f u n c t i o n . H e n c e s k e t c h t h i s f u n c t i o n i n t h e d o m a i n - 2 \leq x \leq 2, g i v e n t h a t t h e r e i s a m a x i m u m t u r n i n g p o i n t a t (\sqrt{2}, 2) .$