HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the derivative of the following w. r. t. x by using method of first principle:

e^2x+1

Find the derivative of the following w. r. t. x by using method of first principle:

3^x 

Find the derivative of the following w. r. t. x by using method of first principle:

log (2x + 5)

Find the derivative of the following w. r. t. x by using method of first principle:

tan (2x + 3)

Find the derivative of the following w. r. t. x by using method of first principle:

sec (5x − 2)

Find the derivative of the following w. r. t. x by using method of first principle:

`x sqrt(x)`

Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:

`sqrt(2x + 5)` at x = 2

Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:

tan x at x = `pi/4`

Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:

`2^(3x + 1)` at x = 2

Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:

log(2x + 1) at x = 2

Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:

`"e"^(3x - 4)` at x = 2

Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:

cos x at x = `(5pi)/4`

Show that the function f is not differentiable at x = −3, where f(x) `{:(=  x^2 + 2, "for"  x < - 3),(= 2 - 3x, "for"  x ≥ - 3):}`

Show that f(x) = x² is continuous and differentiable at x = 0

Discuss the continuity and differentiability of f(x) = x |x| at x = 0

Discuss the continuity and differentiability of f(x) = (2x + 3) |2x + 3| at x = `- 3/2`

Discuss the continuity and differentiability of f(x) at x = 2

f(x) = [x] if x ∈ [0, 4). [where [*] is a greatest integer (floor) function]

Test the continuity and differentiability of f(x) `{:(= 3 x + 2, "if"  x > 2),(= 12 - x^2, "if"  x ≤ 2):}}` at x = 2

If f(x) `{:(= sin x - cos x, "if"  x ≤ pi/2),(= 2x - pi + 1, "if"  x > pi /2):}` Test the continuity and differentiability of f at x = `π/2`

Examine the function

f(x) `{:(= x^2 cos (1/x)",", "for"  x ≠ 0),(= 0",", "for"  x = 0):}`

for continuity and differentiability at x = 0