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    Beginning Calculus (SMN3013)

    Uploaded by

    nurul najwa
    1. The document is the final examination for a Beginning Calculus course at Sultan Idris Education University. It contains 7 questions testing students' skills in topics like limits, derivatives, integrals, and graph sketching. 2. Question 1 has students sketch a piecewise defined function, find a limit, prove continuity and differentiability, and sketch a derivative graph. Question 2 has them find the equation of a tangent line. 3. The last question asks students to set up a sum of definite integrals to find the total shaded area between two curves on a given interval, and then calculate that area between specific functions over a given interval.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Beginning Calculus (SMN3013)

    Uploaded by

    nurul najwa
    70 views3 pages
    1. The document is the final examination for a Beginning Calculus course at Sultan Idris Education University. It contains 7 questions testing students' skills in topics like limits, derivatives, integrals, and graph sketching. 2. Question 1 has students sketch a piecewise defined function, find a limit, prove continuity and differentiability, and sketch a derivative graph. Question 2 has them find the equation of a tangent line. 3. The last question asks students to set up a sum of definite integrals to find the total shaded area between two curves on a given interval, and then calculate that area between specific functions over a given interval.

    Original Title

    BEGINNING CALCULUS (SMN3013) (1)

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    1. The document is the final examination for a Beginning Calculus course at Sultan Idris Education University. It contains 7 questions testing students' skills in topics like limits, derivatives, integrals, and graph sketching. 2. Question 1 has students sketch a piecewise defined function, find a limit, prove continuity and differentiability, and sketch a derivative graph. Question 2 has them find the equation of a tangent line. 3. The last question asks students to set up a sum of definite integrals to find the total shaded area between two curves on a given interval, and then calculate that area between specific functions over a given interval.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    70 views3 pages

    Beginning Calculus (SMN3013)

    Uploaded by

    nurul najwa
    1. The document is the final examination for a Beginning Calculus course at Sultan Idris Education University. It contains 7 questions testing students' skills in topics like limits, derivatives, integrals, and graph sketching. 2. Question 1 has students sketch a piecewise defined function, find a limit, prove continuity and differentiability, and sketch a derivative graph. Question 2 has them find the equation of a tangent line. 3. The last question asks students to set up a sum of definite integrals to find the total shaded area between two curves on a given interval, and then calculate that area between specific functions over a given interval.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
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    CONFIDENTIAL

    �NIVE�ITI
    \m.,.
    u
    L� tl

    --=--
    SDfD1D1K(\N
    lORIS
    ULTAN
    ,-,""J.>I.}.bL�.l;..cl��)
    SlILT,\N IDRIS EDUCATION UNIVERSITY

    UNIVERSITI PENOIOIKAN SULTAN lORIS

    FINAL EXAMINATION
    SEMESTER 2 SESSION 2015/2016

    CODE: SMN3013 COURSE : BEGINNING CALCULUS

    1 5 JUN
    DATE: 2D16 DURATION : 2 HOURS 30 MINUTES

    INSTRUCTIONS
    1. This examination paper contains SEVEN (7) questions.
    2. Answer all questions in the examination booklet. Use a new page for a new question.
    3. Show your work. Marks may be deducted for incomplete work.
    4. Scientific calculator may be used in this examination.
    5. This question paper will be collected at the end of the examination.

    This question paper contains 3 pages including the front page.

    PROGRAMME:

    YEAR: CLASS GROUP:

    REGISTRATION NO. : I I I I I I I
    IDENTITY CARD NO:
    I I I I I I I I I I I I I
    LECTURER(S) : MR. SHAHRIZAL SHAMSUDDIN

    DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO

    CONFIDENTIAL
    2
    SMN3013: Beginning Calculus

    1. Let 1, x � 1
    z --r
    f (x) =

    { �a;, x > 1.

    a. Sketch the graph of f.


    b. Find lim f (x) .

    "' ...... 1
    c. Prove that f is continuous at x = 1.
    d. Prove that f is differentiable at x = 1·
    e. Sketch the graph of f'.

    [15 marks}

    tIle
    curve x2y + 3xy3 -

    X =
    3 at (1,1).
    2. Find the equation of the tangent line to

    [15 marks}

    State your answer in terms of x.


    3. a. Find �� given that y =
    (x3 _

    2x)ln:c .

    [7 marks]

    b. Find �:�, given that y =


    3 sin (2x2 + 1).

    [8 marks}

    4. Evaluate the integrals using any suitable method.

    a.

    [7 marks]

    b.
    J (Inx)2 dx.

    [8 marks)

    +x2 +2
    5. Compute
    JX5 x
    3
    -x
    dx using the method of partial fractions.

    [15 marks]

    [See next page


    SMN3013: Beginning Calculus 3

    6. The graph of the derivative function I' (x) (NOT I (x)) is shown in Figure 1 below.
    Based on this graph, answer the following questions about the function I (x) (NOT
    I' (x)).
    _y

    r= f(x)

    Figure 1

    Estimate:

    a. the intervals on which I


    increasing.is
    b. the intervals on which I
    decreasing.is
    c. the open intervals on which I is concave up.
    d. the open intervals on which I is concave down.
    e. all values of x at which I has an inflection point.
    f. all values of x at which I has relative minima.
    g. all values of x at which I has relative maxima.

    [15 marks]

    7. a. Set up a sum of definite integrals that represents the total shaded area between
    the curves y
    =
    I(x) and y g(x) in Figure 2 below.
    =

    y=g(x)

    Figure 2

    [3 marks]

    b. Find the total area enclosed between y = x3 and y = x over the interval [-1,2J.

    [7 marks]
    END OF QUESTIONS

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