HSC Science (Computer Science) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

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

Select the correct answer from the given alternative:

If y = `("a"x + "b")/("c"x + "d")`, then `("d"y)/("d"x)` =

Select the correct answer from the given alternative:

If f(x) `{:(= 2x + 6, "for"  0 ≤ x ≤ 2),(= "a"x^2 + "b"x, "for"  2 < x ≤4):}` is differentiable at x = 2 then the values of a and b are

Select the correct answer from the given alternative:

If f(x) `{:( = x^2 + sin x + 1, "for"  x ≤ 0),(= x^2 - 2x + 1, "for"  x ≤ 0):}` then

Select the correct answer from the given alternative:

If, f(x) = `x^50/50 + x^49/49 + x^48/48 + .... +x^2/2 + x + 1`, thef f'(1) =

Determine whether the following function is differentiable at x = 3 where,

f(x) `{:(= x^2 + 2","  ,  "for"  x ≥ 3),(= 6x - 7"," ,  "for"  x < 3):}`

Find the values of p and q that make function f(x) differentiable everywhere on R

f(x) `{:( = 3 - x"," , "for"  x < 1),(= "p"x^2 + "q"x",", "for"  x ≥ 1):}`

Determine the values of p and q that make the function f(x) differentiable on R where

f(x) `{:( = "p"x^3",", "for"  x < 2),(= x^2 + "q"",", "for"  x ≥ 2):}`

Determine all real values of p and q that ensure the function

f(x) `{:( = "p"x + "q"",", "for"  x ≤ 1),(= tan ((pix)/4)",", "for"  1 < x < 2):}` is differentiable at x = 1

Discuss whether the function f(x) = |x + 1| + |x  – 1| is differentiable ∀ x ∈ R

Test whether the function f(x) `{:(= 2x - 3",", "for"  x ≥ 2),(= x - 1",", "for"  x < 2):}` is differentiable at x = 2

Test whether the function f(x) `{:(= x^2 + 1",", "for"  x ≥ 2),(= 2x + 1",", "for"  x < 2):}` is differentiable at x = 2

Test whether the function f(x) `{:(= 5x - 3x^2",", "for"  x ≥ 1),(= 3 - x",", "for"  x < 1):}` is differentiable at x = 1

If y = `"e"^x/sqrt(x)` find `("d"y)/("d"x)` when x = 1

Evaluate the limit:

`lim_(x->0)[(sqrt(6+x+x^2) -sqrt6)/x]`

Answer the following:

Find the trigonometric functions of :

90°

Answer the following:

Find the trigonometric functions of :

240°