Calculus Continuity Mock Tests

7 questions available

Calculus Continuity Mock Test 1

Questions: 7

नमूना प्रश्न

JEE Advanced Mathematics

The value of lim(x→0) (sin(x) - x) / x³ equals:

A -1/6

B 1/6

C 0

D 1

JEE Advanced Mathematics

Let f(x) = |x^2 - 1| + |x^2 - 4| for x in R. The number of points where f is not differentiable is

A 2

B 5

C 4

D 3

JEE Advanced Mathematics

Let f(x) = { x^n · sin(1/x) if x ≠ 0; 0 if x = 0 }, where n is a positive integer. Which of the following statements is/are TRUE?

A f is twice differentiable at x = 0 if n >= 4

B The derivative f prime is continuous at x = 0 if and only if n >= 3

C f is continuous at x = 0 if and only if n ≥ 1

D f is differentiable at x = 0 if and only if n >= 1

JEE Advanced Mathematics

Let f(x) = { (sin(ax) + sin(bx))/x for x ≠ 0, a + b for x = 0 }. If f is continuous at x = 0, then:

A f is continuous for all real a and b

B a = b

C a + b = 0

D a = b = 1

JEE Advanced Mathematics

Let f(x) = max{x, x³} for x ∈ ℝ. The set of points where f is not differentiable is:

A {0}

B {0, 1}

C {-1, 0, 1}

D {-1, 1}

JEE Advanced Mathematics

Let f(x) = |x - 1| + |x - 2| + |x - 3| for x in R. Which of the following is/are TRUE?

A f has a global minimum at x = 1

B f is increasing on [1, 2]

C f is differentiable everywhere

D f is continuous everywhere but not differentiable at x = 1, 2, 3

JEE Advanced Mathematics

The number of points where the function f(x) = |x - 1| + |x - 2| is not differentiable is:

A 2

B 1

C 0

D 3

Calculus Continuity Mock Tests

Calculus Continuity Mock Test 1

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