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

Evaluate the following limit :

`lim_(x -> 0) [(cos("a"x) - cos("b"x))/(cos("c"x) - 1)]`

Evaluate the following limit :

`lim_(x -> pi) [(sqrt(1 - cosx) - sqrt(2))/(sin^2 x)]`

Evaluate the following limit :

`lim_(x -> pi/4) [(tan^2x - cot^2x)/(secx - "cosec"x)]`

Evaluate the following limit :

`lim_(x -> pi/6) [(2sin^2x + sinx - 1)/(2sin^2x - 3sinx + 1)]`

Select the correct answer from the given alternatives.

`lim_(x → π/3) ((tan^2x - 3)/(sec^3x - 8))` =

Select the correct answer from the given alternatives.

`lim_(x -> 0) ((5sinx - xcosx)/(2tanx - 3x^2))` =

Select the correct answer from the given alternatives.

`lim_(x -> pi/2) [(3cos x + cos 3x)/(2x - pi)^3]` =

Evaluate the following :

`lim_(x -> 0)[(secx^2 - 1)/x^4]`

Evaluate the following :

`lim_(x -> 0) [(x(6^x - 3^x))/(cos (6x) - cos (4x))]`

Evaluate the following :

`lim_(x -> "a") [(sinx - sin"a")/(x - "a")]`

Evaluate the following :

`lim_(x -> "a") [(x cos "a" - "a" cos x)/(x - "a")]`

Evaluate the following :

`lim_(x -> pi/4) [(sinx - cosx)^2/(sqrt(2) - sinx - cosx)]`

Differentiate the following w.r.t.x. :

y = x⁵ tan x

Differentiate the following w.r.t.x. :

y = (x² + 2)² sin x

Differentiate the following w.r.t.x. :

y = `"e"^xsecx - x^(5/3) log x`

Differentiate the following w.r.t.x. :

y = `x^4 + x sqrt(x) cos x - x^2"e"^x`

Differentiate the following w.r.t.x. :

y = `sinx logx + "e"^x cos x - "e"^x sqrt(x)`

Differentiate the following w.r.t.x. :

y = `"e"^x tanx + cos x log x - sqrt(x)  5^x`

Differentiate the following w.r.t.x. :

y = `(x^2 sin x)/(x + cos x)`

Fill in the blanks:

y = e^x .tan x

Differentiating w.r.t.x

`("d"y)/("d"x) = "d"/("d"x)("e"^x tan x)`

= `square "d"/("d"x) tanx + tan x "d"/("d"x) square`

= `square  square + tan x  square`

= `"e"^x [square  + square]`