Determine the standard equation of the ellipse that satisfies the given properties: center at the origin, a vertex 8 units from a focus and 18 units from the other vertex with vertical principal axis x2 A %3D 96 100 x2. y? В 64 73 © x2 y? = 1 64 63 80 = 1 81

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A: f(x)= e ax f0(ln 7)= 7a   f'(x) =ea x af'(ln 7)=ea ln 7 = a 7a   f' ' (x) =ea x a2f' '(ln 7) = ea ln...

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A: Limit  =  0 When both variable are in sum and squared form then trigonometry subsitution results in ...

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A: ∫exdx1.Integrate with respect to xex+C12.Integrate with respect to x∫(ex+C1)dx=ex+C1x+C23.Integrate ...

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A: an =nn+1a1 = 11+1 a1 =12a2 = 22+1 a2 =23a3 = 33+1 a3 =34a4 = 44+1 a4 =45a5 = 55+1 a5 =56

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A: We want to integrate the given function.

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A: Given query is to find when function is concave up and when concave down.  

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A: This question can be solved by using the concept of finding the slope of tangent at the given point ...

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A: We have to find dydx and d2ydx2.                                              x=t2+3, y=t2+7t

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A: We will evaluate the given integral as shown below by using trigonometric substitution

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A: Here we have to find the limits of the given functions.

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A: Given query is to find the derivative using definition and the equation of tangent at x =2.

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A: We can find the answer as below.  

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A: We can find the integral answer as below.

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A: cos2θ = 1-2sin2θ

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A: Derivatives

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A: limx→af(x),  by completing a table of functional values. step 1: choose two sets of x-values—one set...