When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.03 cm/ min. At what rate is the plate's area increasing when the radius is 40 cm? The rate of change of the area is cm / min. (Type an exact answer in terms of r.)

Q: Find the first derivative of y = 1 using the Chain Rule. (1– x4)6

A: These questions are related to differentiation, We will solve them using given information. 

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A: Follow the procedure given below.

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A: an=n+1-n+3 limn→∞an=limn→∞n+1-n+3limn→∞n+1-n+3=limn→∞n1+1n-n1+3n   =limn→∞n1+1n-1+3n=limn→∞1+1n-1+3n...

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A: We want to find limit of the function. 

Q: what is 2x3

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Q: ded. Give your answers as intervals in the form (*, *). Use symbol iate type of parenthesis " (", ")...

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Q: 7. There is a removable discontinuity at x = 1 and f(1) = 4 8. There is a jump discontinuity at x = ...

A: follow next step 

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Q: Consider the vector field F Evaluate |F. dī along the curve C: 7(t) = tỉ +t°j, 0 <t < 2

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Q: 11.What is the slope of the tangent line to the curve y = 3x? – 5 at poin - O A. -7 О в. -5 O C. -6 ...

A: Differential equation 

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Q: Direction: Read then solve the question carefully. Click the letter of the correct answer. Boyle\T 1...

A: This question is based on differentiation.

Q: Find an upper bound on the error that can result if cos(æ) is approximated by 1– (x/2!) + (x*/4!) ov...

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A: Given, x(y+1)dx+(y/x)2dy=0 Separation of variables means, Seperate x  variables on dx side and y var...

Q: lim log2 ( – &r – 1) 8x – -1) x→-5

A: To evaluate the given limit , substitute  x= -5  in the given expression.

Q: 4. What is the equation of the tangent line to y = sin(sin(x)) at the point (T,0)

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Q: To Sketch the Graphs of functions using Derivatives. Problem. Consider the function f(x) = 8x - x wh...

A: Follow the procedure given below.

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to x - 2x + 36x – 3x + 4)...

A: We have to find the value of n. 

Q: 3. lim 4" 4. lim 5 X +00 5. lim (0.2)* lim (0.2) 6.

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Q: 2. The degree of the differential equation 5x +Sy =0s dr

A: We will find the degree of differential equation in the following step.

Q: Consider the initial value problem and find the solution for y''+4ay'+(4a²y+4y)=0 and y(0)=-2, y'(0)...

A: Solution: y''+4ay'+(4a²y+4y)=0 and y(0)=-2, y'(0)=-1.

Q: The velocity of an object was measured using a laser radar gun. The following data were collected. t...

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Q: 18. lim 19. lim 20. lim log, x

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Q: Find dy/dx by implicit differentiation. x3 + x2y + 7y2 = 4 %3D y' = %3D

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Q: 6) Evaluate each integral. 5x-3 x²-7x+10 | u Sun 7x-x² +11x-3 (x² +1)(x² +3)

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Q: Consider the polar equation r = 4 cos(0) – 13 sin(0). (a) Convert the given polar equation to a Cart...

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Q: Plot the following function as a 3D plot: (x + y)* + (x – y)² - f(x, y) = 2(x + y)² 4

A: Plot the function:f(x,y)=2(x+y)2-(x+y)4+(x-y)24

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A: Given: y=x2 ; y=3x   Now find the point of intersection between the curve and line; x2=3xx2-3x=0xx-3...

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Q: Find the slope of the curve r=7-cos(theta) at theta=9pi/4.

A: I am attaching image so that you understand each and every step.

Q: Differentiate the following implicit equation for y(x) with respect to r: 3x – a°y+ 4y³ = 6

A: Finding dy/dx

Q: 5. Exact Differe ntial Equation: x(3xy-4y' +6dx+(x' -6x'y' -1dy = 0

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Q: find all of the critical points and local maximums and minimums of each function. (d) f(x) = |æ+ 5|....

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Q: Find dy/dx by implicit differentiation. x2 - 5xy + y3 = c y' = %3D

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A: Here, to write the other method to find the arbitrary constant of the differential equation.

Q: 2. f(x) = e2x; a=0, n=10

A: Given:       fx=e2x. a=0, n=10       

Q: Your elderly neighbor places a bag of corn kernels on your doorstep each morning. The first day, the...

A: Given, number of a kernel of coin on                                  the first day = 11            ...

Q: 26.The derivative of a sum is the sum of the derivatives. AEalse. B.True

A:

Q: 3. Integration by parts: 3x d x (V3 2x+4

A: To find out the integration.