Educational

# 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.

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 .

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

Question: The concept of fundamental to calculus.

Question: The relationship between two variables is called

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

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

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 .

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

Question: The concept of fundamental to calculus.

Question: The relationship between two variables is called

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

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

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?

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

If \$$f(x)=xA2-3x\$$, evaluate \$$f(-5)\$$

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

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

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

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?

If \$$f(x)=xA2-3x\$$, evaluate \$$f(-5)\$$

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?

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

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 ?

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

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?

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.

Question: Find\$$\\lim_{x\\to2}\\frac{xA{2H} {x-2}\$$\n\$$\\lim_{x\\to2}\\frac{xA{2HKx- 2}\$$\n

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

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

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

Question: A polynomial function is at every real number.

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

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

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

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