Highest voted questions in Engineering Mathematics

2 votes
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1
Which one of the following functions is analytic over the entire complex plane?$\ln(z)$$e^{1/z}$$\frac{1}{1-z}$$\cos(z)$
1 votes
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6
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7
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12
Evaluate the limit\[\lim _{n \rightarrow \infty}\left(2 n^{4}\right)^{\frac{1}{3 n}} .\]$e$$1$$2^{\frac{1}{3}}$$0$None of the above
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13
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14
The matrix\[A=\left(\begin{array}{ccc}1 & a_{1} & a_{1}^{2} \\1 & a_{2} & a_{2}^{2} \\1 & a_{3} & a_{3}^{2}\end{array}\right)\]is invertible when$a_{1}>a_{2}>a_{3}$$a_{1}...
1 votes
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21
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24
What is\[\lim _{n \rightarrow \infty} \cos \frac{\pi}{2^{2}} \cos \frac{\pi}{2^{3}} \cdots \cos \frac{\pi}{2^{n}} ?\]$0$$\pi / 2$$1 / \sqrt{2}$$2 / \pi$None of the above....
1 votes
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36
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is convex if for $x, y \in \mathbb{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq \alpha f(x)+(1-\alpha) f(y)$.Which...
1 votes
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37
The minimum value of $f(x)=\ln \left(1+\exp \left(x^{2}-3 x+2\right)\right)$ for $x \geq 0$, where $\ln (\cdot)$ denotes the natural logarithm, is$\ln \left(1+e^{-1 / 4}\...
1 votes
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38
Let $\alpha_{1}, \alpha_{2}, \cdots, \alpha_{k}$ be complex numbers. Then\[\lim _{n \rightarrow \infty}\left|\sum_{i=1}^{k} \alpha_{i}^{n}\right|^{1 / n}\]is$0$$\infty$$\...
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40