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MTH102 – Elementary Mathematical II Past Question and Answer

MTH102 - Elementary Mathematical II Past Question and Answer

MTH102 – Elementary Mathematical II Past Question and Answer
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Question: Given that \\(f(x)=2x-4\\)\nand\\ (g(x)=xA{2}+3\\) then \\(f\\left ( gWIeft ( x Wright ) Wright )W)\nis\n
Answer: W(2xA{2}-2\\)

Question: A function is , if every horizontal line intersect the graph of the function atmost once.
Answer: One to one

Question: If \\(xA{2}+5x+5\\) then \\ (f(x+2)\\)\nis\n
Answer: \\(xA{2}+9x+19\\)

Question: Suppose \\(f(x)=xA{3}\\) then \\ (fA{-1}(x)\\)\nis\n
Answer: \\(\\sqrt[3]{x}\\)

Question: \\(\\lim_{x\\to 1 }\\frac{\\left | x-1 Wright |Xx-1}\\) does .
Answer: Not exist

Question: Which of the following is NOT a function?
Answer: \\(x+yA{2}=1\\)

Question: The concept of fundamental to calculus.
Answer: Limit

Question: The relationship between two variables is called
Answer: Function

Question: \\(\\lim_{x\\to-2}\\left ( xA{2}+3 Wright )\\)
Answer: 7

Question: Given that f(x)=2xA{2}-4x+1\\)> then f(-1) is
Answer: 7

Question: If \\(xA{2}+5x+5\\) then \\ (f(x+2)\\)\nis\n
Answer: \\(xA{2}+9x+19\\)

Question: Given that \\(f(x)=2x-4\\)\nand\\ (g(x)=xA{2}+3\\) then \\(f\\left ( gWIeft ( x Wright ) Wright )W)\nis\n
Answer: W(2xA{2}-2W)

Question: A function is , if every horizontal line intersect the graph of the function atmost once.
Answer: One to one

Question: \\(\\lim_{x\\to 1 }\\frac{\\left | x-1 Wright |Xx-1}\\) does .
Answer: Not exist

Question: Which of the following is NOT a function?
Answer: \\(x+yA{2}=1\\)

Question: The concept of fundamental to calculus.
Answer: Limit

Question: The relationship between two variables is called
Answer: Function

Question: Given that f(x)=2xA{2}-4x+1\\)> then f(-1) is
Answer: 7

Each value taken on by the dependent variable of a function is called ?
Answer: image

Use the approximate method to find \\ (lim_{x\\rightarrow 0}5xA2(1-cosx)\\)
Answer: \\(0\\)

Determine the \\(lim_{x\\rightarrow p}\\frac{xA3-pA3Kx-p}\\)
Answer: \\(3pA2\\)

Obtain the derivative of \\(bxAn\\), where \\ (b\\) is a constant and \\(n\\) is a positive integer
Answer: \\(bnxA{n-1}\\)

For what value of \\(x\\) is the function \\ (\\frac{1Kx-2}\\) not defined?
Answer: 2

Let \\(f(x)=xA2+2\\) and \\(g(x)=2x+1\\), find \\ (f(g(x))\\)
Answer: \\(4xA2-16x+16\\)

If \\(y=xA5eAx\\), find W(\\frac{dyKdx}\\) Answer: \\(\\frac{dx}{dy}=xA{4}eA{x}(x+5)\\)

If \\(X\\) and \\(Y\\) are non-empty sets in the function \\(f : XWrightarrow Y, the set \\(X\\) is called
Answer: domain of the function

If \\(f(x)=xA2-3x\\), evaluate \\(f(-5)\\)
Answer: 40

If W(y=sec7xA{2}\\), find \\(\\frac{dy}{dx}\\)
Answer: \\(14xtan7xA2sec7xA2\\)

If \\(A\\) and \\(B\\) are non-empty sets in the function \\(G:A\\rightarrow BW), the set \\(B\\) is called
Answer: codomain of the function

Find the value of \\(f(x)=xA2-5x+1\\) when \\ (x=4\\)
Answer: -3

If two functions agree at all but a single point c (i.e. x = c), then they have?
Answer: identical limit

Obtain the derivative of \\(bxAn\\), where \\ (b\\) is a constant and \\(n\\) is a positive integer
Answer: \\(bnxA{n-1}\\)

For what value of \\(x\\) is the function \\ (\\frac{1Kx-2}\\) not defined?
Answer: 2

If \\(f(x)=xA2-3x\\), evaluate \\(f(-5)\\)
Answer: 40

Discuss the continuity of \\(f(x)=\\sqrt{3-x}\\)
Answer: \\(x<3\\)

If a discontinuity function \\(f\\) can be made continuous by appropriately redefining \\(f (c)\\) is called?
Answer: removable

Determine the \\(lim_{x\\rightarrow p}\\frac{xA3-pA3Kx-p}\\)
Answer: \\(3pA2\\)

If \\(X\\) and \\(Y\\) are non-empty sets in the function \\(f : XWrightarrow Y, the set \\(X\\) is called
Answer: domain of the function

If W(y=sec7xA{2}\\), find W(\\frac{dyKdx}\\)
Answer: \\(14xtan7xA2sec7xA2\\)

If \\(y=xA5eAx\\), find W(\\frac{dyKdx}\\) Answer: \\(\\frac{dx}{dy}=xA{4}eA{x}(x+5)\\)

Which of the following equations define \\ (y\\) as a function of \\(x\\)?
Answer: \\(x+y=1\\)

Evaluate \\(lim_{x\\rightarrow \\infty}\\frac{2xA3+5xA2-3x+1K6xA3-x+5}\\)
Answer: \\(\\frac{1K3}\\)

Find the inverse relationship of the function \\(y=2x+5\\)
Answer: \\(x=\\frac{1}{2}(y-5)\\)

Let \\(f(x)=xA2+2\\) and \\(g(x)=2x+1\\), find \\ (f(g(x))\\)
Answer: \\(4xA2-16x+16\\)

Each value taken on by the dependent variable of a function is called ?
Answer: image

What is the value of the limit \\ (lim_{x\\rightarTow 0}\\frac{xA2-x-2}{xA2-2x}\\)
Answer: doesnot exist

If to each value of the dependent variable in the range there is corresponding exactly one value of the independent variable, the function is called?
Answer: one to one

Use the approximate method to find \\ (lim_{x\\rightarrow 0}5xA2(1-cosx)\\)
Answer: \\(0\\)

Obtain the \\(lim_{x\\rightarrow 2}\\frac{x^2-x-2}{x^2-2x}\\)
(A)\\(0\\)
(B)1
(C)\\(\\frac{3}{2}\\)
(D)Undefined

Ans: \\(\\frac{3}{2}\\)

If the value of the function \\(y(x)\\) get arbitrary close to \\(b\\) as \\(x\\) approaches the point \\(a\\) , the statement can be mathematically written as
(A)\\(lim_{x\\rightarrow b}y(x)=a\\)
(B)\\(lim y(x)=b-a\\)
(C)\\(lim_{x\\rightarrow a}y(x)=b\\)
(D)\\(lim y(x)=a-b\\)

Ans: \\(lim_{x\\rightarrow a}y(x)=b\\)

Determine the diffenetiation of 120
(A)\\(0\\)
(B)120
(C)\\(x\\)
(D)\\(120x\\)

Ans: \\(0\\)

What is the inverse of thee function \\(y=x^2\\)
(A)\\(x=y^{1/2}\\)
(B)\\(x=y^2\\)
(C)\\(x=2y\\)
(D)\\(x=\\frac{1}{2}y^2\\)

Ans: \\(x=y^{1/2}\\)

If \\(x^x\\), find \\(\\frac{dy}{dx}\\)
(A)\\(lnx\\)
(B)\\(1+lnx\\)
(C)\\(x(1+lnx)\\)
(D)\\(x^x(1+lnx)\\)

Ans: \\(x^x(1+lnx)\\)

Obtain the range of \\(f(x)=\\sqrt{9-x^2}\\) for which \\(f(x)\\) is a reaal function
(A)\\(0\\leq x\\leq 3\\)
(B)\\(x\\geq 3\\)
(C)\\(-3(D)\\(-3\\leq x \\leq 3\\)

Ans: \\(0\\leq x\\leq 3\\)

Differentiate with respect to \\(t\\) the function \\(f(t)=3c0s2t\\)
(A)\\(-3sin2t\\)
(B)\\(6cos2t\\)
(C)\\(2sin3t\\)
(D)\\(-6sin2t\\)

Ans: \\(-6sin2t\\)

8).If \\(p\\) is a polynomial function and \\(c\\) is any real number, then
(A)\\(lim_{x\\rightarrow c}p(c)=p(x)\\)
(B)\\(lim_{x\\rightarrow c}p(c)=0\\)
(C)\\(lim_{x\\rightarrow c}p(c)=\\infty\\)
(D)\\(lim_{x\\rightarrow c}p(c)=p(x)\\)

Ans: \\(lim_{x\\rightarrow c}p(c)=p(x)\\)

Evaluate the derivative of \\(y(x)=x^2\\) at the point \\(x\\)
(A)\\(2x^2\\)
(B)\\(2x\\)
(C)\\(x^2\\)
(D)2

Ans: \\(2x\\)

Determine the equation that defines \\(y\\) as a function of \\(x\\).
(A)\\(y^2-2y=-1\\)
(B)\\(x-y=2\\)
(C)\\(2y^2+x=1\\)
(D)\\(y^2+2x^2=3\\)

Ans: \\(x-y=2\\)

Question: \\(f(x)=\\frac{1KxA{2}+1}\\) is continuous on the entire line.
Answer: real

Question: Find\\(\\lim_{x\\to2}\\frac{xA{2H} {x-2}\\)\n\\(\\lim_{x\\to2}\\frac{xA{2HKx- 2}\\)\n
Answer: 4

Question: EvaluateW (\\lim_{x\\to1 }\\frac{xA{2}-1 «x-1 }\\)\n
Answer: 3

Question: Using the replacement theorem, evaluate W(\\lim_{x\\to0}\\frac{\\sqrt{x+1 }-1} {x}\\)\n
Answer: \\(\\frac{1X2}\\)

Question: Evaluate W(\\lim_{x\\to2} (x^{2}-2x+3)\\)\n
Answer: [C] 3

Question: The derivative of\\ (y=xA{2}+3x\\)\nusing first principle
Answer: \\(2x+3\\)

Question: Evaluate\\(\\lim_{x\\to-3}\\frac{5} {x+3}\\)\n
Answer: \\(\\infty\\)

Question: The process of obtaining the derivative of a function is called
Answer: differentiation

Question: A polynomial function is at every real number.
Answer: continous

Question: Evaluate \\ (\\lim_{x\\to3}\\frac{xA{2}+x-6Kx+3}\\)\n
Answer: 1

Question: \\(f(x)=\\frac{1KxA{2}+1}\\) is continuous on the entire line.
Answer: real

Question: Using the replacement theorem, evaluate W(\\lim_{x\\to0}\\frac{\\sqrt{x+1 }-1} {x}\\)\n
Answer: \\(\\frac{1X2}\\)

Question: if \\(y=\\left ( 2x+8 Wright )A{3}W)\nthenW(Wfrac{dyKdx}W)\nis
Answer: \\((2x+8)^{2}\\)

Question: If \\(y=x^{4}-6x^{3}-4x^{2}\\) then\\ (\\frac{dy}{dx}\\)\nat\\(x=2\\)\nis\n
Answer: \\(-56\\)

Question: If \\(2xA{2}+3yA{2}=10\\)\nthen \\ (\\frac{dyKdx}\\)\nis
Answer: \\(-\\frac{4x}{6y}\\)

Question: If \\(y=sin\\left ( 5x-6 Wright )W)\nthenW(Wfrac{dyKdx}W)\nis
Answer: \\(5cos\\left ( 5x-6 \\right )\\)

Question: If \\(y=xA{4}-6xA{3HxA{2}\\) thenW (\\frac{dyKdx}\\)\nat\\(x=2\\)\nis\n
Answer: \\(-56\\)

Question: If \\(y=ïïleft ( 3x-1 Wright )A{3}W)\nthenW(Wfrac{dyKdx}W)\nis
Answer: \\(9\\left ( 3x-1 \\right )^{2}\\)

Question: Differentiate \\(-2eA{-4x}\\)\n
Answer: \\(8e^{-4x}\\)

Question: Differentiate \\(\\left ( 3x-2 Wright )\\left ( xA{2} +3Wright )\\)\n
Answer: \\(9x^{2}-4x+9\\)

Question: The derivative of\\(tan\\theta\\)\nis
Answer: \\(sec^{2}\\theta\\)

Question: Differentiate \\(y=\\frac{sinx} {cosx}\\)\n
Answer: \\(sec^{2}x\\)

Question: of a straight line graph \\ (m=\\frac{\\delta y}{delta y}\\)\n
Answer: Gradien

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