On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

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Q: Differentiate the following hyperbolic functions

A: Consider the given hyperbolic function y=log5sinh e9x2.

Q: Find the equation of the tangent plane to the surface 4 =1 at the point 9. 16 (1,-3,2)

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A: Given equation: x2+y2=r2                     . . . (1) (a) Differentiating (1) with respect to x,…

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A: Given function isWe have to find a standard equation for the tangent plane to the graph of f at the…

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Q: Find the length (in units) of the curve y =    16 − x2between x = 0 and x = 2.

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Q: Find y in terms of x. dy = x 2 + 5, curve passes through (0, 14) dx x3 A) y = + 5x 3 B y = x3 + 5x +…

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Q: Find all intersections of the curve y = 10 - x and y = x + 8.

A: To find intersection point of the curves.

Q: At which point/s does the graph of y = r+9 have a horizontal tangent line? Write the point/s in the…

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Q: Assume that y is a function of x. Find (d2y)/(dx2) for x2y-y2-2(sqrt x)+4=0 at point (1,2) 7/6 8/6…

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Q: For what values of a and b will the parabola y=x² + ax + b be tangent to the curve y=x³ at the point…

A: Note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Let f(x, y) = 5ex - Y. Find the equation for the tangent plane to the graph of f at the point (5,…

A: Given: fx, y=5ex-y. To Find: Equation of tangent plane to the graph of f at the point 5, 5.

Q: Determine the magnitude and direction of the largest change 2 2 (x² + y²)z at the point M (1, -2,1).…

A: Introduction How sharply a curve rises determines its magnitude. It is simplest just examine the…

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Q: Find all the values of x at which the curve y = xe xe-6x? has stationary points. %3D Give your…

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Q: Explain the geometric meaning of r'(t).

A: Let the function is given as ,  rt=ft, gt, ht The derivative of the function is, r't=f't, g't, h't…

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 7z2 = 27,   (−3,…

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Exponential Growth Model

The relation that represents an exponential function is: