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3
votes
1
answer
25k
views
1
answer
Prove that $\bar{F} = \frac{r}{r^3}$ is both irrotational and solenoidal.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.4k
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1
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If $\bar{A} = \bar{V}(xy + yz + zx)$ find $\bar{V}\cdot \bar{A}$ and $\bar{V} \times \bar{A}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.3k
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Evaluate following using appropriate theorem $\int\int\limits_{s}(9x\bar{i} + 6y\bar{j} - 10z\bar{k})$ where s is the surface of sphere with radius 2 units.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.5k
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1
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Evaluate the following by using appropriate theorem $\int Fdr$ where $\bar{F} = (2x - y)\hat{i} - (yz^2)\hat{j} - (y^2 z)\hat{k}$ and c is the boundary of upper half of sphere $(x^2 + y^2 + z^2) = 4$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
vote
1
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21k
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1
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Prove that the angle between two surface $x^2 + y^2 + z^2 = 9$ and $x^2 + y^2 - z = 3$ at the point (2, -1, 2) is $cos^{-1}\bigg(\frac{8}{3\sqrt{21}}\bigg)$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
2
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1
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46k
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1
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Find the constants a,b,c so that $\bar{F} = (x + 2y + az)\hat{i} + (bx - 3y - z)\hat{j} + (4x + cy + 2z)\hat{k}$ is irrotational
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
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1
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2.6k
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1
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Find the work done in moving a particle in a force field given by $\bar{F} = 3xy\hat{i} - 5z\hat{j} + 10x\hat{k}$ along the cirlce $x = t^2 + 1, y = 2t^2, z = t^3$ from t = 1 to t = 2
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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10.0k
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1
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A vector field $\bar{F}$ is given by $\bar{F} = (x^2 - yz)\hat{i} + (y^2 - zx)\hat{j} + (z^2 - xy)\hat{k}$ is irrotational and hence find scalar point function $\phi$ such that $\bar{F} = \bar{V}\phi$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.3k
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Evaluate by green's theorem $\oint\limits_{c} (x^2 yax + y^3)dy$ where C is closed path formed by y = x, y = $x^2$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.4k
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Find the directional derivative of d = $x^2 ycosz$ at $(1,2,\frac{\pi}{2})$ in the direction of $\bar{a} = 2\bar{i} + 3\bar{j} + 3\bar{k}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.2k
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1
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If $\bar{F} = xye^{2x}\bar{i} + xy^2 cosz\bar{j} + x^2 cosy\bar{k}$ find div $\bar{F}$ & curl $\bar{F}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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9.2k
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1
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Prove that $\log\sec x=\dfrac {x^2}2+\dfrac {x^4}{12}+\dfrac {x^6}{45}+ --------$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.8k
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1
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Fit a straight line passing through points $(0,1), (1,2) , (2,3),(3,4.5),(4,6),(5,7.5)$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.4k
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1
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Evaluate: $$\lim_{x\to 0} \Bigg[ \dfrac{1}{x^2}-cot^2x \Bigg]$$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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1.4k
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1
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Evaluate: $$ \lim_{x\to 0} (1+tanx)^{cotx} $$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
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6.2k
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1
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$$ \lim_{x\to 0} \dfrac{asinh x + b sinx}{x^3} \;=\; \dfrac{5}{3} $$ , find a and b.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
answer
23k
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1
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By using Taylor' series,expand $ tan^{-1} x$ in positive powers of (x-1) upto first four non-zero terms.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
answer
1.3k
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1
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Evaluate $$ \lim_{x\to 0} \dfrac{sinx \cdot sin^{-1}x - x^2}{x^6} $$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
5
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1
answer
89k
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1
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Fit a second degree parabolic curve to the following data:
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
2
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1
answer
11k
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1
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Fit a straight line to the following data and estimate the production in the year 1957:
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
vote
1
answer
2.1k
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1
answer
Fit a curve $y=ax+bx_2$ for the data:
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
answer
7.9k
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1
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Fit a straight line to the following data with x as independent variable.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
0
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1
answer
6.7k
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1
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Fit a straight line to the following data: (x,y)=(-1,-5),(1,1),(2,4),(3,7),(4,10). Estimate y when x=7.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
vote
1
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18k
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1
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Fit a straight line for the following data:
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
3
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1
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14k
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1
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Jacobians : If $ ux=yz , \; vz=yx , \; wz = xy \; , \; find \; J\Big( \frac{ u,v,w }{x,y,z} \Big) $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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