S Use Trigonometric Substitution to find the indefinite integral O 4v Y 4- y² y² 4(4- y²) + C O √4-y² 4y O sin ¹()+C 1 4- y² + C + C dy (4- y²) 3/2

Q: Let f(x) = x for x < 0 and f(x) = sin(x) for x ≥ 0. Match the following. Here DNE means does not…

A: The function is  f(x)=x for x &lt; 0 and f(x)=sin(x) for x≥0

Q: DETAILS The velocity of a skydiver, in feet per second, t seconds after jumping out of an airplane,…

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Q: On the interval shown, for which graph is f' positive and f"' negative? OA. OB. Q O C. z Q 2 OD.

A: To choose the graph which describes the given characteristics

Q: Integrate using u-substitution or 2 guys in Jail. fx sin(2x²) dx 5. (4x³-2)7 (24x²)dx

A: (4)   I=∫xsin(2x2)dx∫sinxdx=-cosx+cdxndx=nxn-1

Q: sing the method of variation of parameters to olve the nonhomogeneous DE: y" + 6y + 25y = 7+ 2x² we…

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Q: (x) = x4−256x+4 Enter the x-values of any local minima, maxima, and inflection points.

A: Given f(x) = x4−256x+4

Q: A brick wall makes two legs of a right angle, one 32 feet long and the other 72 feet long. A…

A: Let's find maximum area and it's dimensions.

Q: ) If we would like to solve the following differential equation by variation of parameters 3x then…

A: We check whether the statement is correct or not .

Q: Assume f and g are functions such that f(x) dx O 5G(x) - 2x + C OG (5x-2) + C O 5G(5x-2) + C OG(a) +…

A: Please see the below picture for detailed solution.

Q: If ƒ(x) = 4x² – 5eª, find: ƒ'(x) = f'(1) = ƒ''(x) = f''(1) =

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Q: Consider statements I, II and III below on antiderivatives. I. If we know one antiderivative of a…

A: Explained below

Q: f(x) = x4−32x−12  Determine where the function is concave up and concave down. Enter your answers…

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Q: 1. (6413 #4 p. 351) The cross section of a large tank is a trapezoid. The short side of the…

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Q: Solve: y (cosx)= (9+ y²)

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Q: Find the derivative of the function. y = sin ¹(cos-¹(t))

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Q: 3 x³e2x dx

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Q: A tank is full of water. Find the work W required to pump the water out of the spout. Use the fact…

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Q: Differentiate. f'(t) = f(t) = 8t t³t-1

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Q: Determine the 3 axis direction angles of force F in the direction of the vector AB when A = (3,1,8)…

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Q: 8) Write the first 5 lines of Pascal's triangle. Use the triangle to find (2x+3)4.

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Q: Consider the following function: Step 4 of 4: Enter the x-values of any local minima, maxima, and…

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Q: Obtain the differential equation of the family of plane curves described and sketch several…

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Q: 4) Set up the partial fraction decomposition of (x− 1)(x+2)(x² +1) Do not solve.

A: Given; (2x3-1)/[(x-1)(x+2)(x2+1)2].

Q: locity of 6. Find the average value of f(2x - 1)³dx.

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Q: Newton's Law of Cooling. The initial temperature of an object is 37.8 degree C. If it took 10…

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Q: Find the length of the cardioid r = 3+3 cos 0. The length of the cardioid is (Simplify your answer.)

A: formula for  length of cardioid is  L=∫abr2+(drdθ)2dθgiven  r=3+3cosθdcosθdθ=-sinθ

Q: Question 1: Find an explicit formula for the geometric sequence with a₁ = 10 and a4 = 80. a_n=…

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Q: Find the equation of the line through the point (-5, 4) and perpendicular to the line y = 2-5.…

A: In this question, we want to find a equation of the line perpendicular to the given line passing…

Q: Let C be the curve f(x) = = the length of C, as follows: (2) Show that √1+ f'(x)² In(x) 2 1 2x x 2 4…

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Q: Determine which graph corresponds to the area enclosed by the curves y= O O Find the area of the…

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Q: F(s) = 9s² 2s - 3 12s + 20

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Q: Find 5 [(7x³ + 3x³) dz

A: use the algebraic property of integrals.

Q: Evaluate the limit, or type "DNE" if the limit Does Not Exist: x²-xy √x-√Y lim (x,y) → (3,3)

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Q: A drone flies with velocity v(t) = 3ti-fj+4k. When t = 1, the drone is at (3,2,2).

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Q: en the graph below, solve the following inequality: g(r) > 0 +10 + 80 9 8 7 -8-7-6-5-4-3 54 6543 2…

A: Given query is to solve the inequality.

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = surface x =…

A: given  z=3x2+y2x=ey

Q: The function f is a continuous function with the following characteristics: f'(x) 0 on the interval…

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Q: Sketch the region R and compute ff 2xdxdy, where R is the region bounded by x = y² and (x-1)² + y² =…

A: To find:- ∬R2xdxdy Where R is the region bounded by x=y2, x-12+y2=1

Q: The graphs of two functions are shown with the areas of the regions between the curves indicated. y…

A: We have to find the required area by using the graph

Q: 1. Evaluate: 1 1+x+x\ L₂FF dr

A: Given integral is ∫-2111+x+xdx

Q: Graph the circle given below by moving the key points: To graph the circle, drag the center point to…

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Q: Find the area of the given region. Use a graphing utility to verify your result. y = 1 + In x³ X y 1…

A: We can find the area of the region .

Q: If g(x) = f* √u² + 2 du, what is d²g / dx²? 0

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Q: For what values of h are the given vectors linearly dependent? 5 -20 -3 12 5 4 6 52 3 h Vectors are…

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Q: A firefly is flying along the path defined by r(t) = 20. At hat point(s) along the firefly's path…

A: Given position vector r( t ) = { t2 , 5-t2 , t3 } r( t ) = t2i + ( 5-t2 )j + t3kas we know that a( t…

Q: Refer to the graph of y = f(a) with secant line PQ and tangent line PS. O PQ O PR O QR OQS OOO…

A: By the definition of dy  dy = f(x+ ∇ x) - f(x)

Q: Inverse Laplace transform of 2 s-5 2 + is s²+16 s³ f(t) = 2cos(4t)-5sin(4t)+t² F(s) = Select one: O…

A: We are required to find if the inverse Laplace transform of F(s) is True or False

Q: A student council consists of 8 students, with 3 women and 5 men. a. In how many ways can a…

A: Members in student council = 8 Number of women in council(w) = 3 Number of men in council(m) = 5

Q: In 1994, the moose population in a park was measured to be 4490. By 1999, the population was…

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Q: Which of the following graphs show a removable discontinuity? (Select all that apply) U e

A: Please see the below answer.