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Section 1: Functions of Several Variables
Section 2: Limits and Continuity
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Engineering Mathematics I
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Practice Problems for Module 5
Practice Problems for Module 5
Sections 3.1 and 3.2
Directions.
The following are review problems. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. You can also follow the link for the full video page to find related videos.
Differentiate the functions.
\(f(x)=\dfrac{7}{4}x^4-3x^2+12\)
\(H(u)=(3u-1)(u+5)\)
Answer
\(f'(x)=7x^3-6x\)
\(H'(u)=3u^2+14u-5\)
Video
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MLC WIR 20B M151 week4 #1ab
\(F(r)=\dfrac{8}{r^3}\)
\(y=\dfrac{\sqrt[3]{x}+x}{x^2}\)
Answer
\(F'(r)=-24r^{-4}\)
\(y'=-\dfrac{5}{3}x^{-8/3}-x^{-2}\)
Video
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MLC WIR 20B M151 week4 #1cd
\(k(x)=e^x+x^e\)
Answer
\(k'(x)=e^x+ex^{e-1}\)
Video
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MLC WIR 20B M151 week4 #1e
\(f(x)=(3x^2-x)e^x\)
Answer
\(f'(x)=(6x-1)e^x+(3x^2-x)e^x\)
Video
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MLC WIR 20B M151 week4 #1f
\(y=\dfrac{e^x}{4-e^x}\)
Answer
\(y'=\dfrac{e^x(4-e^x)-e^x(-e^x)}{\left(4-e^x\right)^2}\)
Video
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MLC WIR 20B M151 week4 #1g
\(G(x)=\dfrac{x^2-3}{5x+1}\)
Answer
\(G'(x)=\dfrac{(2x)(5x+1)-(x^2-3)(5)}{(5x+1)^2}\)
Video
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MLC WIR 20B M151 week4 #1h
\(F(y)=\left( \dfrac{1}{y^2}-\dfrac{3}{y^4}\right)\left(y+2y^3\right)\)
Answer
\(F'(y)=\left(-2y^{-3}+12y^{-5}\right)\left(y+2y^3\right)+\left(y^{-2}-3y^{-4}\right)\left(1+6y^2\right)\)
Video
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MLC WIR 20B M151 week4 #1i
\(V(t)=\dfrac{7+t}{te^t}\)
Answer
\(V'(t)=\dfrac{(1)\left(te^t\right)-(7+t)\left(e^t+te^t\right)}{\left(te^t\right)^2}\)
Video
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MLC WIR 20B M151 week4 #1j
Find \(f'(x)\) and \(f''(x)\) for \(f(x)=\left(x^3+1\right)e^x\).
Answer
\(f'(x)=\left(x^3+3x^2+1\right)e^x\)
\(f''(x)=\left(3x^2+6x\right)e^x +\left(x^3+3x^2+1\right)e^x\)
Video
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MLC WIR 20B M151 week4 #2a