HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

Solve using intermediate value theorem:

Show that 5^x − 6x = 0 has a root in [1, 2]

Solve using intermediate value theorem:

Show that x³ − 5x² + 3x + 6 = 0 has at least two real root between x = 1 and x = 5

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

x² + 3x – 1

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

sin (3x)

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`