12 Mathematics Calculus Differentiability Test 03 5t3q5m

CBSE TEST PAPER-04 CLASS - XII MATHEMATICS (Calculus: Continuity and Differentiability) Topic: - Differentiation

1.

Discuss the continuity of the function

-2,  f ( x ) = 2x, 2, 

if if if

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x ≤ -1 -1 < x ≤ 1 x>1

2.

Find

dy sin(ax + b) if y = dx cos( cx + d )

3.

Find

dy if dx

4.

Find

1 dy , if y= ( x cos x ) x + ( x sin x ) x dx

5.

t dy  x = a  cos t + log tan  , y = a sin t find 2 dx 

6.

d 2 y  dy  If e ( x + 1) = 1 show that =  dx 2  dx 

7.

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 3x − x 3  y = tan −1  2   1 − 3x 

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2

y

y=a

t+

t 2

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a

t dy  and x =  t +  Find dx  2

8.

 1 + sin x + 1 − sin x  y = cot −1    1 + sin x − 1 − sin x 

9.

If y = cos x + cos x + cos x + ........ Prove that (1 − 2 y )

10.

dy π x  − sec x = 0 y = log tan  +  Show that dx  4 2

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dy = sin x dx

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