HSC Science कक्षा ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions

Show that the following functions are not differentiable at the indicated value of x.

`f(x) = {{:(-x + 2, x ≤ 2),(2x - 4, x > 2):}` , x = 2

Show that the following functions are not differentiable at the indicated value of x.

`f(x) = {{:(3x",", x < 0),(-4x",", x ≥ 0):}` , x = 0

The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable.

If f(x) = |x + 100| + x², test whether f’(–100) exists.

Examine the differentiability of functions in R by drawing the diagram

|sin x|

Examine the differentiability of functions in R by drawing the diagram

|cos x|

Choose the correct alternative:

f y = f(x² + 2) and f'(3) = 5 , then `("d"y)/("d"x)` at x = 1 is

Choose the correct alternative:

If f(x) = x² – 3x, then the points at which f(x) = f’(x) are

Choose the correct alternative:

If y = mx + c and f(0) = f’(0) = 1, then f(2) is

Choose the correct alternative:

If f(x) = x + 2, then f'(f(x)) at x = 4 is

Choose the correct alternative:

If pv = 81, then `"dp"/"dv"` at v = 9 is

Choose the correct alternative:

It is given that f'(a) exists, then `lim_(x -> "a") (xf("a") - "a"f(x))/(x - "a")` is

Choose the correct alternative:

If f(x) = `{{:(x + 1,  "when"   x < 2),(2x - 1,  "when"  x ≥ 2):}` , then f'(2) is

Choose the correct alternative:

If g(x) = (x² + 2x + 1) f(x) and f(0) = 5 and `lim_(x -> 0) (f(x) - 5)/x` = 4, then g'(0) is

Choose the correct alternative:

If f(x) = `{{:(x + 2, - 1 < x < 3),(5, x = 3),(8 - x, x > 3):}` , then at x = 3, f'(x) is

Integrate the following with respect to x:

x¹¹ 

Integrate the following with respect to x:

`1/x^7`

Integrate the following with respect to x:

`root(3)(x^4)`

Integrate the following with respect to x:

`(x^5)^(1/8)`

Integrate the following with respect to x:

`1/(sin^2x)`