Set up and evaluate the integral for the area of the shaded region. y=x²-3x² - 40x ... X Evaluate the integral to find the area of the shaded region. (Type an integer or a simplified fraction.)

Q: Find r(t) for the given conditions. r(t): r"(t) = -4 cos(t)j - 5 sin(t)k, r'(0) = 5k, r(0) = 4j

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Q: 2. Find the exact values or state that the expression is undefined ¹(3) b. os¯¹(1.5) a. sin-1 c.…

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Q: Find the interval of convergence of the series. (x − 7)″ 2+8n Σ n=0 OA. 2<x< 12 OB. -1≤x≤15 O C.…

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Q: Part II. 1) y = cos(2x) sin(x) 2) y sin²(x) cot²(x) 3) y = 2 cos(x) − 6 sec(x) +3

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Q: Determine whether each of the following vector fields F⃗ F→ is path independent (conservative) or…

A: use partial derivative for checking the path independent.

Q: Differential Calculus Find the third derivative of the ff: 1) y x 1-ex 2) y = 2ex - 8x 3) y = 6ex -…

A: We have to find the third derivative of the given function.

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

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Q: 5x50 3 £ =ㅅ

A: The given curve is  y=x33,  0≤x≤3

Q: You borrow $950 from a payday loan office for 15 months. They charge you simple interest at a rate…

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Q: Given the function f(x) = - x2 - 4x - 3 a) What is the maximum value of the function? Why? b) What…

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Q: bair of dice is rolled. What is the probability of getting a sum of 11? What is the probability of…

A: Given query is to find the probability of getting 11.

Q: Find the volume of the solid that results when the region bounded by the curve x = y² and the curve…

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Q: Find the following limits for f (x) lim f(x) = 0 x-4 If necessary, select the most informative…

A: Given query is to find indicated limit.

Q: Differentiate y = eª — x² arctan x.

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Q: Let f(x) = x³ - 13x. Calculate the difference quotient f(3+h)-f(3) for h h = .1 h = .01 h = .01 h =…

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Q: If f(x) = et and 8(x) = xe~_e= Find the inner product of f (x) and g(x) on the interval [0, 2]

A: The functions are: fx = exgx = xe-x-e-x To evaluate: The inner product of fx and gx on the interval…

Q: Evaluate. S dx x² √9-x²

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Q: Use upper and lower sums to approximate the area of the region using the given number of…

A: Solve the following

Q: Problem 7. Evaluate the definite integral. |s² - 5s +6| ds.

A: To evaluate the given integral

Q: 9.x = 1 -1 (1) -)₁ X 3 2-1 2 1-1,

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Q: (²x(4²√x + 5√x) dx

A: The given integral ∫01x4x3+5x4dx. We have to evaluate this integral.

Q: Consider the following. = sin(10), y = cos (a) Eliminate the parameter to find a Cartesian equation…

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Q: Find the cost function for the marginal cost function. C'(x) = 0.04e0.02x; fixed cost is $10 C(x) =

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Q: Find the inverse, if it exists, for the given matrix. 52 21 www Select the correct choice below and,…

A: To find the inverse of the given matrix A.

Q: Express the limit as a definite integral on the given interval. 2x;* + (x;*)² Ax, [1, 6] lim n→∞ dx

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim e9ti + sin(6t)j + e-2tk…

A: To find the limit of the given function

Q: The function g is defined as follows. g(x)= (a) = Find the following limits. If a limit does not…

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Q: Evaluate. Assume u> 0 when In u appears. 10) f(x5-2x4)4 (5x4-8x³) dx

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Q: Suppose the slope of the curve y = f¯¹ (x) at the point (4,7) is . Find ƒ'(7). [B] 4 [A] 1 [C] 5 [D]…

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Q: 4. Given u = (-2, 5) and v= (6,-8), find a. u + v b. 2v- u C. U. V d. ||v||

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Q: We can use L'Hopital's Rule to calculate lim X18 x³ + 2x ₂3 2x²

A: limx→∞x3+2x2x2we know that indeterminant forms is 00,  ∞∞, 0×∞, 00, ∞0, 1∞ and ∞-∞

Q: 9. Use Law of Sines to solve AABC with B = 17°, a = 3, and b = 1. Round the measures of the unknown…

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Q: 2² Calculate Rn for f(x) = - R + 6 on the interval [0, 4] and write your answer as a function of n…

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Q: Use a parametrization to express the area of the surface as a double integral. Then evaluate the…

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Q: 3. y = 1+5x Inx

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Q: . Find the area between the curvey = x² and the straight line y = 8x - 4.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the total differential. dw = w = eбy cos(4x) + z10

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Q: A = 3+i4 ii) A if i) A + B * & B = 530 B iii) (A/B)-¹ find:

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Q: The volume of the sphere is increasing at the rate of 6 cubic centimeters per hour. At what rate is…

A: Let Volume of sphere = V Area of sphere = A radius of sphere = r V = 43πr3A = 4πr2Given r = 47 cm…

Q: Use the information to find and compare Ay and dy. (Round your answers to four decimal places. y =…

A: formula used ∆y=f(x+∆x)-f(x)dxndx=nxn-1

Q: (a) The series For the following answer blanks, decide whether the given sequence or series is…

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Q: Evaluate x+3 x²+x-2 X x²+4x+4 2x²+11x+15

A: Given: So,…

Q: Given values for x and z to be -12 and 2, evaluate the following ordered triples to determine the…

A: Given system of equation 2x - 4y - 3z = -2 y = x3 - 3 -2x + 2y -4z = 2

Q: ← Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= 6 cos…

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Q: Which one of the following integrals gives the length of the parametric curve x(t) = t², y(t) = = =…

A: As we know that length of the curve from a to b  L = ∫ab( dxdt )2 + ( dydt)2dtGiven  x = t2y = 2t 0…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: The given curves are  x=4-y2,  x=y2-4

Q: Convert the rectangular equation to an equation in cylindrical coordinates and spherical…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y=x√√√3-x² dy =

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Q: Let z = √xy + 2x²y³. The slope of the line tangent to the curve of intersection of the surface given…

A: The surface given is  z=xy+2x2y3

Q: Use 1 + tan² x = sec² x to evaluate tan xsec4 xdx

A: To evaluate the given integral