Draw the level curves for the function z = f(x, y) given by z = /4 – x² – y² when z = 0, 1, 2 and then, sketch the graph of %3D -

Q: Directions: Differentiate the following functions. 5.) y = In(x* + 5) 6.) f(x) = x*e3% %3D

A: 5)y=lnx4+56) fx=x4e3xTo find its differentiation

Q: Determine the concavity of the graphs of y^2=x and y=x^3

A: We have to determine the convexity of the graphs of y2 = x and y = x3 in between the points of their…

Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

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Q: Consider the function h (x) = 2x^2 – 8x – 10. Find its vertex

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Q: The graph attached shows the curves y = x^2 and y^2=x. a.) Discuss the similarities and differences…

A: Here we have to give the differences and similarities between the two graphs that is y=x2  and x=y2.

Q: sketch the graph of function Xy-y-1=0

A: xy-y-1=0 we can draw the graph of the function

Q: Sketch the graph of y = 4x/(x + 1)2, x > -1.

A: To sketch the graph of y=4xx+12, x>-1 Since x>-1, we consider values of x greater than 1, and…

Q: Determine the equation of the vertical trace of the function g(x,y)=-x^2-y^2+2x+4y-1 corresponding…

A: To find equation of vertical trace we need to substitute value of variable in the given equation of…

Q: Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis and a tangent…

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Q: Calculate facterial funchion n -X x e %3D

A: Using integration by parts solve the integral:  ∫0∞xne-xdx=∫xne-xdx0∞…

Q: Differentiate and simplify. f(x)=Je* +In (x² +4)

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Q: Sketch the graph of the following function.   Find . dy/dx and d^2y/dx^2 Draw number lines showing…

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Q: Find the slope of the graph of the function x2+y2=xy+1/4 at (1/2 , 1/2)

A: Given function is Differentiating both sides with respect to x, we get

Q: Which of the following graphs (a)-(d) could represent an antiderivative of the function shown in…

A: We need to determine the antiderivative of the function in the graph. We know that ∫xndx=xn+1n+1+C.

Q: Consider the function f(x)=x^5 - 5x^4 a. Find where the function is increasing and decreasing.…

A: Increasing and Decreasing functions : If f'(x)>0 for every x on some interval ,then f(x) is…