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Define limit of a function. Find limit \(\lim_{x \to ∞} (x – \sqrt{x}) \)
Answered
Mathematics I
Define cross product of two vectors. If \(\vec{a} = \vec{i} + 3\vec{j} + 4\vec{k}\) and \(\vec{b} = 2\vec{i} + 7\vec{j} – 5\vec{k}\) find the vector \(\vec{b} \times \vec{a} \enspace and \enspace \vec{a} \times \vec{b}\)
Answered
Mathematics I
Test the convergence of the series \(\sum_{n=1}^{∞} \left ( \frac{n^n}{n!} \right )\)
Answered
Mathematics I
Find the solution of y”+6y’+9=0, y(0)=2, y'(0)=1
Answered
Mathematics I
Find the length of the arc of the semi cubical parabola y
2
= x
2
between the points (1,1) and (4,8)
Answered
Mathematics I
Determine whether the integral \(\int_{1}^{∞}\left ( \frac{1}{x} \right )dx\) is convergent or divergent
Answered
Mathematics I
Sketch the curve y = x^3 + x
Answered
Mathematics I
Verify Mean Value Theorem by f(x) = x
3
– 3x + 3 for [-1, 2]
Answered
Mathematics I
Use Continuity to evaluate the limit, \(\lim_{x \to 4} \left ( \frac{5 + \sqrt{x}}{\sqrt{5 + x}} \right )\)
Answered
Mathematics I
If \(f(x) = \sqrt{x}\) and \(g(x) = \sqrt{3-x}\), find gof and gog.
Answered
Mathematics I
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