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Limits and Derivatives

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Intuitive Idea of Derivatives

Subtopic

Intuitive Idea of Derivatives under Limits and Derivatives for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the derivative of the constant function f(x)=5f(x) = 5 with respect to xx?

    A.

    55

    B.

    00

    C.

    11

    D.

    5x5x

  2. 2.

    If the function f(x)=x2f(x) = x^2 represents the area of a square with side length xx, what is the instantaneous rate of change of the area with respect to the side length when x=3x = 3?

    A.

    33

    B.

    99

    C.

    00

    D.

    66

  3. 3.

    In the graph of a function y=f(x)y = f(x), what does the value of the derivative at a point PP intuitively represent?

    A.

    The yy-coordinate of the point PP

    B.

    The area under the curve from the origin to PP

    C.

    The slope of the tangent to the curve at PP

    D.

    The shortest distance from the point PP to the origin

Download the worksheet for Limits and Derivatives - Intuitive Idea of Derivatives to practice offline. It includes additional chapter-level practice questions.

Limits

Subtopic

Limits under Limits and Derivatives for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find lim⁡x→0(1+x+x2)\lim_{x \to 0} (1 + x + x^2).

    A.

    0

    B.

    1

    C.

    2

    D.

    Undefined

  2. 2.

    Evaluate lim⁡x→01−cos⁡2xx2\lim_{x \to 0} \frac{1 - \cos 2x}{x^2}.

    A.

    1

    B.

    2

    C.

    0

    D.

    1/2

  3. 3.

    What is lim⁡x→−1x3+1x+1\lim_{x \to -1} \frac{x^3 + 1}{x + 1}?

    A.

    0

    B.

    3

    C.

    1

    D.

    -3

Download the worksheet for Limits and Derivatives - Limits to practice offline. It includes additional chapter-level practice questions.

Limits of Trigonometric Functions

Subtopic

Limits of Trigonometric Functions under Limits and Derivatives for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Determine the value of: lim⁡x→01−cos⁡axx2\lim_{x \to 0} \frac{1 - \cos ax}{x^2}

    A.

    aa

    B.

    a2a^2

    C.

    a/2a/2

    D.

    a22\frac{a^2}{2}

  2. 2.

    Evaluate the limit: lim⁡x→0sin⁡(x/4)x\lim_{x \to 0} \frac{\sin (x/4)}{x}

    A.

    44

    B.

    14\frac{1}{4}

    C.

    11

    D.

    00

  3. 3.

    Find the value of lim⁡x→πsin⁡2xsin⁡x\lim_{x \to \pi} \frac{\sin 2x}{\sin x}

    A.

    22

    B.

    −2-2

    C.

    00

    D.

    11

Download the worksheet for Limits and Derivatives - Limits of Trigonometric Functions to practice offline. It includes additional chapter-level practice questions.

Derivatives

Subtopic

Derivatives under Limits and Derivatives for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the derivative of f(x)=(x−1)(x−2)f(x) = (x-1)(x-2).

    A.

    2x−32x - 3

    B.

    2x+32x + 3

    C.

    x−3x - 3

    D.

    2x−22x - 2

  2. 2.

    Calculate ddx(xcos⁡x)\frac{d}{dx} (x \cos x).

    A.

    cos⁡x−xsin⁡x\cos x - x \sin x

    B.

    cos⁡x+xsin⁡x\cos x + x \sin x

    C.

    sin⁡x−xcos⁡x\sin x - x \cos x

    D.

    −sin⁡x-\sin x

  3. 3.

    Determine the derivative of f(x)=x2−2sin⁡xf(x) = x^2 - 2\sin x.

    A.

    2x−2cos⁡x2x - 2\cos x

    B.

    2x+2cos⁡x2x + 2\cos x

    C.

    x2−2cos⁡xx^2 - 2\cos x

    D.

    2x−cos⁡x2x - \cos x

Download the worksheet for Limits and Derivatives - Derivatives to practice offline. It includes additional chapter-level practice questions.

Algebra of derivative of functions

Subtopic

Algebra of derivative of functions under Limits and Derivatives for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the derivative of f(x)=x2+2xf(x) = \frac{x}{2} + \frac{2}{x}.

    A.

    12+2x2\frac{1}{2} + \frac{2}{x^2}

    B.

    12−2x2\frac{1}{2} - \frac{2}{x^2}

    C.

    1−2x21 - \frac{2}{x^2}

    D.

    12−1x2\frac{1}{2} - \frac{1}{x^2}

  2. 2.

    If aa is a constant, find the derivative of f(x)=sin⁡(x+a)f(x) = \sin(x+a).

    A.

    cos⁡(x+a)\cos(x+a)

    B.

    cos⁡x+cos⁡a\cos x + \cos a

    C.

    −cos⁡(x+a)-\cos(x+a)

    D.

    sin⁡(x+a)\sin(x+a)

  3. 3.

    Determine the derivative of f(x)=x2+1xf(x) = \frac{x^2+1}{x} by dividing first.

    A.

    1+1x21 + \frac{1}{x^2}

    B.

    1−x21 - x^2

    C.

    1−1x21 - \frac{1}{x^2}

    D.

    2x2x

Download the worksheet for Limits and Derivatives - Algebra of derivative of functions to practice offline. It includes additional chapter-level practice questions.