For the function f (x) = xe¬*: a) Determine the coordinates of the critical point. Use exact values. b) Use the first derivative test (Chart method / Number line) to determine if the critical point is a local minimum or a local maximum.

Q: Consider the following functions. f(x) g(x) = 8 sin x = 8 cos 2x | 2 6

A: The objective of the question is evaluate the area of the given bounded region.

Q: Find T(t) and N(t) at the given point. r(t) = 9 cos(t)i +9 sin(t)j + tk; t = 2 || T(;) N ||

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Q: 17) Find the area of the serface genereted by revolving tue curr X> 3t, y=2t about fue x-Qx's on tue…

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Q: Sol V= cotcex) dx /2

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Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x²…

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Q: follmcing IVP yi = 42-5unt y= - 44,+17 cost Q.5. O Solve 30こ5,4,(0)22

A: A detailed solution is given below.

Q: d Calculate ri(t) r2(t)] and rı(t) x r2(t)] first by differentiating dt the product directly and…

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Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: Given the vectors A = 3i – 5j + 2k and B = 7i + j – 2k. Find the vector projection of A onto B.

A: Given : A→=3i-5j+2kB→=7i+j-2k     To Find : Vctor Projection of A→  onto B→

Q: Evaluate lim, (-5x + 5 – 5 - ) 12 O + O 5 O-5

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Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: A company manufactures rope, and the total cost of producing r feet of rope is Cr dollars.To…

Q: What is the equation of the tangent plane normal to x2 + y2 + z = 9 at the point (1, 2, 4)? O 2x -…

A: Given; f(x,y,z)=x^2+y^2+z-9  Point (1,2,4)

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: 4 P = R What is the rate of change of power with respect to resistance? rate of change = Viohm?

A: Given problem:- The power, P, dissipated when a 2-volt battery is put across a resistance of R ohms…

Q: Calculus

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Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. p…

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Q: 27 10

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: Use Riemann Sums to calculate the area under the curve over the interval (1,3] for f(x) = x² + 2

A: By using Reimann Sums to calculate the area under the curve over the interval 1, 3 for fx=x2+2.

Q: (D² + 4)y=12; y(0) = 0 , y'(0) = 2 %3D

A: (D2+4)y=12

Q: The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick, use…

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Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 5…

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Q: Find V· (V × F), if F(x, y, z) = 3e**i+3xe'j – 3e²k. - V·(V × F)

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Q: Verify Green's Theorem by evaluating both integrals ÔN I y? dx + x2 dy = dA ay ax 'R for the given…

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Q: 0.09 ) 12t At the end of t years, the future value of an investment of $37,500 in an account that…

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Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. (x?2 - х) dx x2 + x +1

A: ∫01x2-xx2+x+1dxit is a improper fraction ( degree of Numerator= Degree of denominator)Using long…

Q: 5.) Matching : Match the terms at the right with the best term on the left that matches it. Secant…

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Q: dx хV х2+2х-1

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Q: Find the first partial derivatives with respect to x,y and z. f(x. y.z) - 3x°y - 9 xyz + 10 yz %3D

A: Find first partial derivative

Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 %3D O x- y…

A: The solution is given in the next step.

Q: Calculate the first eight terms of the sequence of partial sums correct to four decimal places. E…

A: We can solve as follows

Q: 3 da Evaluate a+2 A. 3 B. 2 С. 1 D. 0

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Q: Verify Green's Theorem by evaluating both integrals ƏN dA y? dx + x² dy = ay for the given path. C:…

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Q: 2. Find an equation of the plane containing the point P(0, –,÷) and the line determined by the two…

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Q: 13) wnite the crroesponding recferge equation for tue curve represenfed dy tue parametic equatias x=…

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Q: Answer the questions for the following polar equation. 3 r 3= 3+10cos0 (a) Identify the conic as a…

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Q: 8 3. y2 = x and y² = 2 – x (Answer: S. U. ) 3 - -

A: Given: y2=x and y2=2-x   Now find the point of intersection between the given curves. y2=x,…

Q: QUESTION 10 If you have $51,000 in student loans at an interest rate of 3%, compounded monthly, what…

A: Solution:

Q: a/a + b/b 189 a/b + b/a = 180 Find a and b value

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Q: Find the norm (or length) of v = <-2, 3)

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Q: Find the curvature of r(t) = 5(cos t) i + 12(sin t) j + tk at t = m/2. Ok = 8/13 Ok = 5/13 O k =…

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Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: We have to find the slope.

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A: Here, the amount of the clay is fixed. dVdt=0...(1) Now, the volume of the cylinder is given by:…

Q: 2. Find an equation of the plane containing the point P (0, -) and the line determined by the two…

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Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = e10ti + e-*j K(t) =

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Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: Given problem:- Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in…

Q: d Calculate ri(t) r2(t)] and rı(t) x r2(t)] first by differentiating dt the product directly and…

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Q: Solve the following integrals: 1. S 7e*dx 4. S 12*+1dx 5. S-dx 2. S(5ex – 6*)dx 3. Ј 3(5)dx 6.…

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