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Prove that $\log\sec x=\dfrac {x^2}2+\dfrac {x^4}{12}+\dfrac {x^6}{45}+ --------$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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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 5.7 years ago by teamques10 ★ 70k
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Evaluate: $$\lim_{x\to 0} \Bigg[ \dfrac{1}{x^2}-cot^2x \Bigg]$$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Evaluate: $$ \lim_{x\to 0} (1+tanx)^{cotx} $$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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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 5.7 years ago by teamques10 ★ 70k
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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 5.7 years ago by teamques10 ★ 70k
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Evaluate $$ \lim_{x\to 0} \dfrac{sinx \cdot sin^{-1}x - x^2}{x^6} $$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Fit a second degree parabolic curve to the following data:
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Fit a straight line to the following data and estimate the production in the year 1957:
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Fit a curve $y=ax+bx_2$ for the data:
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Fit a straight line to the following data with x as independent variable.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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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 5.7 years ago by teamques10 ★ 70k
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Fit a straight line for the following data:
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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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 5.7 years ago by teamques10 ★ 70k
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Jacobians : If $ u=1-x , \; v=x(1-y) , \; w = xy(1-z) \; , \; Show \; that \; \frac{\partial (u,v,w) }{\partial (x,y,z)} \; = \; -x^2y $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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If $ x = rcos\theta \; y=rsin\theta. \; Find \frac{\partial (x,y) }{\partial (r,\theta)} $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Jacobians : If $ u = \frac{x+y}{1-xy} , \; v \; = \; tan^{-1}x \; + \; tan^{-1}y , \; Find \frac{\partial (u,v)}{\partial (x,y)} $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Jacobians : If $ x=e^v sec \; u \; , \; y=e^v tan \; u, Find \; J\bigg ( \frac{u,v}{x,y} \bigg) $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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If $U=xyz, V=x^2+y^2+z^2, W=x+y+z $ Then prove that $\dfrac {dx}{dU}=\dfrac 1{(x-y)(x-z)}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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If $x=r\sin \theta\cos\phi,y=r\sin\theta\sin\phi z=r\cos \theta $ then find $\dfrac {d(r,\theta\phi)}{d(x,y,z)}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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State and prove Euler's theorem for three variables and hence find the following
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Euler Theorem : If $ x+y=2e^{\theta} cos\phi \;, \; \; x - y \;=\; 2ie^{\theta} sin\phi \; \;$and u is a function of $x$ and $y$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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State and prove Euler theorem for a homogeneous function in two variables and hence find $x\dfrac{\partial u}{\partial x}+y\dfrac{\partial u}{\partial y} \; if\;u=\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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State and prove Euler theorem for a homogeneous function in two variables and hence find the value of following :
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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State and prove Euler theorem for a homogeneous function in two variables and find $ x\dfrac{\partial u}{\partial x}+y\dfrac{\partial u}{\partial y} \;\; where\;u=\dfrac{\sqrt{x}+\sqrt{y}}{x+y} $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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