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Find the directional derivative of  at point  in the direction of vector. Where

 ,  and

F(x,y,z)=z-x/z+y, p (3,4,-5) and u= 2i+6j-k



Find the directional derivative of  at point  in the direction of vector. Where

 ,  and

F(x,y,z)=z-x/z+y, p (3,4,-5) and u= 2i+6j-k



For which values of a and b is the line b 2x + y = tangent to the parabola 2

y = ax

when x = 2? (2) 

 


1). show that fourier series of f(t) = a^2/t(t/2- τ) is given by the f(t) = a^2/t _∑_(-∞)^∞▒〖(a^2/π^(2n^2 ) x^i2πnfτ)〗Does the function holds for only odd values of n


solve the differential equation dy/dx + y cos x = y^3sin2x


solve the diffrential equation x dy/dx + y = x^2y^6


Write the equation of each conic section with the given properties:

A hyperbola with foci at (15,0) and (-15,0) and asymptotes y = 3/4x and y = -3/4x


A rectangle plot of land is to be fenced off so that the area enclosed will be 400 ft2

. Let 

L

be the 

length of fencing needed and 

x

the length of one side of the rectangle. Show that

L ="2x" + (800/x)

for 𝑥 > 0. What is the shortest possible length of such a fence?


Let R* and R** are two partial orders defined on set s check wether R*and R** is partial order on same set S


Intergate completely.

∫(4x^5-15x^4-x^3+12x^2+2x+3)/(x^2-3x-2)dx


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