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Calculus

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

Limits of Polynomials, Rational, Trigonometric, Exponential and Logarithmic Functions

Subtopic

Limits of Polynomials, Rational, Trigonometric, Exponential and Logarithmic Functions under Calculus for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Evaluate: lim⁑xβ†’010xβˆ’1x\lim_{x \to 0} \frac{10^x - 1}{x}

    A.

    10

    B.

    1

    C.

    log⁑e10\log_{e} 10

    D.

    0

  2. 2.

    Evaluate the limit: lim⁑xβ†’βˆ’1x2βˆ’1x+1\lim_{x \to -1} \frac{x^2 - 1}{x + 1}

    A.

    0

    B.

    -2

    C.

    2

    D.

    -1

  3. 3.

    Evaluate: lim⁑xβ†’0sin⁑4xtan⁑4x\lim_{x \to 0} \frac{\sin 4x}{\tan 4x}

    A.

    1

    B.

    4

    C.

    0

    D.

    1/4

Download the worksheet for Calculus - Limits of Polynomials, Rational, Trigonometric, Exponential and Logarithmic Functions to practice offline. It includes additional chapter-level practice questions.

Derivatives as a rate of change

Subtopic

Derivatives as a rate of change under Calculus for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the rate of change of the area of a circle with respect to its diameter DD. (Area A=Ο€D24A = \frac{\pi D^2}{4})

    A.

    Ο€D2\frac{\pi D}{2}

    B.

    Ο€D\pi D

    C.

    Ο€4\frac{\pi}{4}

    D.

    2Ο€D2\pi D

  2. 2.

    The power PP in a circuit with constant voltage V=10V = 10 is P=10IP = 10I, where II is the current. Find the rate of change of power with respect to current.

    A.

    10I10I

    B.

    1010

    C.

    11

    D.

    00

  3. 3.

    Find the rate of change of the area of a circle with respect to its circumference when the radius is 5Β units5\text{ units}.

    A.

    55

    B.

    1010

    C.

    2.52.5

    D.

    5Ο€5\pi

Download the worksheet for Calculus - Derivatives as a rate of change to practice offline. It includes additional chapter-level practice questions.

Derivatives of Polynomial and Trigonometric Functions

Subtopic

Derivatives of Polynomial and Trigonometric Functions under Calculus for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the derivative of f(x)=cot⁑xβˆ’5xf(x) = \cot x - 5x?

    A.

    csc⁑2xβˆ’5\csc^2 x - 5

    B.

    βˆ’csc⁑2xβˆ’5-\csc^2 x - 5

    C.

    βˆ’csc⁑xcot⁑xβˆ’5-\csc x \cot x - 5

    D.

    sec⁑2xβˆ’5\sec^2 x - 5

  2. 2.

    Find the derivative of f(x)=2x2βˆ’cos⁑xf(x) = 2x^2 - \cos x.

    A.

    4xβˆ’sin⁑x4x - \sin x

    B.

    4x+sin⁑x4x + \sin x

    C.

    2x+sin⁑x2x + \sin x

    D.

    4x+cos⁑x4x + \cos x

  3. 3.

    What is the derivative of f(x)=x+xf(x) = \sqrt{x} + x?

    A.

    12x+1\frac{1}{2\sqrt{x}} + 1

    B.

    1x+1\frac{1}{\sqrt{x}} + 1

    C.

    2x+12\sqrt{x} + 1

    D.

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

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