MTH102: Elementary Mathematics Ii TMA2

MTH102: Elementary Mathematics Ii TMA2

Instructions: Answer All .
After Submission, you will not be able to answer these questions

Question 1 : Given $$\frac{2x^5+x^2-5}{t^2}$$

, find $$\frac{dy}{dx}$$ by using the first principle
$$6t+7t^{-3}$$
$$t^2+5t^{-3}$$
c$$-t^{-2}+8t^{-3}$$
$$6t^2+10t^{-3}$$

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Question 2 : Evaluate the limit $$limx\to \infty \frac{6e^{4x}-e^{-2x}}{8e^{4x}-e^{2x}+3e^{-x}}$$
$$\frac{3}{4}$$
$$\frac{3}{5}$$
$$\frac{1}{4}$$
$$\frac{1}{2}$$

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Question 3 : Evaluate the limit $$limx\to -\infty \frac{x^2-5t-9}{2x^4+3x^3}$$
4
2
0
1

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Question 4 : Evaluate the limit $$limx\to \infty \frac{2x^4-x^2+8x}{-5x^4+7}$$
$$\frac{1}{3}$$
$$\frac{2}{3}$$
$$\frac{1}{2}$$
$$\frac{3}{4}$$

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Question 5 : Find the derivative $$f\left(x\right)=2x^2-16x+35$$ by using first principle
$$4x-16$$
$$x+16$$
$$2x-8$$
$$3x-5$$

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Question 6 : Evaluate the limit $$limx\to -\infty \frac{x^2-5t-9}{2x^4+3x^3}$$
2
1
0
4

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Question 7 : Differentiate $$y=3\sqrt{(}{x}^2\left)\right(2x-x^2)$$ with respect to x
$$y=\frac{10x^{\frac{2}{3}}}{3}+\frac{8x^{\frac{5}{3}}}{3}$$
$$y=\frac{5x^{\frac{2}{3}}}{3}+\frac{4x^{\frac{5}{3}}}{3}$$
$$y=\frac{5x^{\frac{2}{3}}}{3}-\frac{4x^{\frac{5}{3}}}{3}$$
$$y=\frac{10x^{\frac{2}{3}}}{3}-\frac{8x^{\frac{5}{3}}}{3}$$

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Question 8 : Evaluate the limit $$limx\to \infty \frac{2x^4-x^2+8x}{-5x^4+7}$$
$$\frac{3}{4}$$
$$\frac{1}{3}$$
$$\frac{1}{2}$$
$$\frac{2}{3}$$

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Question 9 : Given $$y\left(x\right)=x^4-4x^3+3x^2-5x$$, evaluate $$\frac{d^{4}y}{d{x}^4}$$
42
30
22
24

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Question 10 : Evaluate the limit $$limt\to 4\frac{t-\sqrt{(}3+4)}{4-t}$$
$$\frac{3}{4}$$
$$\frac{-1}{8}$$
$$\frac{-3}{8}$$
$$\frac{-5}{8}$$

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Question 11 : Evaluate the limit $$limx\to \infty \frac{6e^{4x}-e^{-2x}}{8e^{4x}-e^{2x}+3e^{-x}}$$
$$\frac{3}{5}$$
$$\frac{1}{4}$$
$$\frac{3}{4}$$
$$\frac{1}{2}$$

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Question 12 : Differentiate with respect to x: $$f\left(x\right)=(ax{}^3+bx)$$
$$a{x}^2+b$$
$$3a-b$$
$$3a{x}^2+b$$
$$3x^2+1$$

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Question 13 : Given $$y\left(x\right)=x^4-4x^3+3x^2-5x$$, evaluate $$\frac{d^{4}y}{d{x}^4}$$
30
22
24
42

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Question 14 : Evaluate the limit $$limt\to 4\frac{t-\sqrt{(}3+4)}{4-t}$$
$$\frac{-3}{8}$$
$$\frac{-5}{8}$$
$$\frac{-1}{8}$$
$$\frac{3}{4}$$

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Question 15 : Differentiate $$y=3\sqrt{(}{x}^2\left)\right(2x-x^2)$$ with respect to x
$$y=\frac{10x^{\frac{2}{3}}}{3}-\frac{8x^{\frac{5}{3}}}{3}$$
$$y=\frac{5x^{\frac{2}{3}}}{3}+\frac{4x^{\frac{5}{3}}}{3}$$
$$y=\frac{10x^{\frac{2}{3}}}{3}+\frac{8x^{\frac{5}{3}}}{3}$$
$$y=\frac{5x^{\frac{2}{3}}}{3}-\frac{4x^{\frac{5}{3}}}{3}$$

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Question 16 : Differentiate with respect to x: $$f\left(x\right)=(ax{}^3+bx)$$
$$a{x}^2+b$$
$$3a-b$$
$$3x^2+1$$
$$3a{x}^2+b$$

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Question 17 : Evaluate the limit $$\underset{h\to 0}{lim}\frac{2(-3+h{)}^2-18}{h}$$
8
6
14
12

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Question 18 : Find the derivative $$f\left(x\right)=2x^2-16x+35$$ by using first principle
$$4x-16$$
$$3x-5$$
$$2x-8$$
$$x+16$$

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Question 19 : Evaluate the limit $$\underset{h\to 0}{lim}\frac{2(-3+h{)}^2-18}{h}$$
6
12
14
8

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Question 20 : Given $$\frac{2x^5+x^2-5}{t^2}$$, find $$\frac{dy}{dx}$$ by using the first principle
$$6t+7t^{-3}$$
$$t^2+5t^{-3}$$
c$$-t^{-2}+8t^{-3}$$
$$6t^2+10t^{-3}$$

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