Tutorial Exercise Evaluate the integral. Step 1 [₁ 10 sin²(x) cos³(x) dx Since [10 10 sin²(x) cos³(x) dx has an odd power of of cos(x), we will convert all but one power to sines. We know that cos²(x) = - sin²(x).

Q: 3. Differentiate the following exponential function without simplifying f(x)=√(e*)(2x)

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Q: Find the area of the region enclosed by y = 3.25x and x = 7.5-y². 2 2 1 2 w A 5 6 N Use horizontal…

A: The area bounded by the curves x= f(y) , x= g(y) between y= a and y = b is given by A = ∫abfy-gy dy

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: Let ux² then dx = du 2x and so 2 2 du S ƒ ze²³d² = ƒ re² de S xe dr xe" 2x 0 0 1 S = (²-1) e" du

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Q: 2x cos(x²) esin(x²) dx

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Q: 2 Rewrite cosx - sin³x cosx using only one trig function. Be sure to simplify.

A: To rewrite the expression cos x - sin2x × cos x ,using only one trigonometric function, we can…

Q: PART III: Solve the following problems. 2. The sum of two positive numbers is 2. Find the smallest…

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Q: [200] Given E=1 42, determine, L3 3 1 1 the determinant of E. 2 the matrix of the minors. 3 the…

A: E=200142331

Q: The least common multiple of the monomials 8a³x6 4a²x6y, abx³y² is: O(a) 8a³x6y² (b) 8a¹bxy2 O(c)…

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Q: -10 x f(x) 10 10 Use interval notation to determine where f(x) ≤ 0. (0,1) 10 Use interval notation…

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Q: Compute the improper integral DNE 1 e e e 1 x ln(x) -dx if it exists. If not, select DNE.

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Q: (7) Given the graph of f(x) below, state the value of the following limits if they exist y

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Q: 10 a) Find the simplified form of the difference quotient for the function f(x) = b) Complete the…

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Q: A tank, shaped like a cone has height 4 meters and base radius 3 meters long. It is placed so that…

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Q: Consider a right triangle with a side of length opposite angle A, a side of length y opposite angle…

A: Given: Consider a right triangle with a side of length x opposite angle A, a sideof length y…

Q: Determine and sketch the domain of the function f(x,y)=√xy.

A: f(x,y)=√(xy)

Q: (a) Find a simplified form of the difference quotient and (b) complete the following table. f(x)=x²…

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A: Given Trigonometric expression  ( 1 - sinx )( 1 + cscx ) = cscx - sinx

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A: We are given a graph of a function rx.We need to find the following limits:limx→8297-rx,…

Q: Let f(x) = 2x³ - 3x² - 72x+1. a. Find all points on the graph of f(x) at which the tangent line is…

A: Let fx=2x3-3x2-72x+1 (a) To find all the points on the graph of fx at which the tangent  lines are…

Q: 1. Which of the following is NOT true about how f(x) = sin³¹(−4(x+6)) + 8 compares with its parent…

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Q: (c) Use the Chain Rule to compute af s^3t^9 + 3s^3 t^12 + 2st Əs In (c) express your answer in terms…

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Q: The population of a city is modeled by the equation P(t) = 479,442e0.1t where t is measured in…

A: The population of a city is modeled  by the equation  P( t ) = 479442e0.1t Where t is measured in…

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A: A lake initially contains 5000 fish. Suppose that in the absence of predators or other causes of…

Q: f(1) = 1 ƒ'(1) = 2 ƒ'(3) = -5 (a) Chain Rule: h(x) = f(g(x)) ⇒ (b) Product Rule: h(x) = f(x) · g(x)…

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Q: What is the complex number z = -3 + 3√3i represented in polar form? Enter your answer by filling in…

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Q: 5n-2 =1\3n+4/ 100 n= 2n+11

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Q: 2. (By partial fractions} Answer: In |x|- 1 x+1 +C ·x² + 3x + 1 x(x + 1)² dx

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Q: Solve the following differential equations dy dr² dy -9x+24y=0, y(1)= 1,y(1) = 0 dx

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Q: (a) Let R > 5 and let CR be the closed, anticlockwise contour obtained by joining the line segment…

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Q: Which of the following could represent an exponential function of the form y=f(x) = A.bx, where b>1?…

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Q: Find the intercepts and the vertical asymptote of Enter the intercepts as points, (a, b). The…

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Q: Σ(-1)" √TI 2n + 3

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Q: Decide from the graph whether a limit exists. If a limit exists, find its value lim F(x) x→-2

A: If the limit exist then the left hand limit and right hand limit are equal

Q: Q Use horizontal strips to find the area, that is, integrate with respect to y. = First find the y…

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Q: 4. (a) (i) Determine the Maclaurin series for sin (2²) up to 2¹4 term. (You may use the Maclaurin…

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Q: 3 What is f S₂² 1+1/2² dx ?

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Q: ₁²√3x²2dx, u = 3x² - 2 du

A: Use the u-subsituation

Q: -g(x) = x¹/3 — x-2/3

A: g(x) = x1/3 -  x-2/3

Q: Let Find e such that lim f(t) exists. t 2 The cis f(t) = 4 1 2t t + c for t 2

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Q: Find a formula for a cubic function f if f(3) = 24 and f(−1) = f(0) = f(4) = 0.

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Q: When finding the moment produced by a three-dimensional force we commonly use the equation M = r X…

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Q: What is an antiderivative of the function x + 2xln(x)? x²ln(x)+2023 xln(x) +2023 In(x) + x xsin(x) +…

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Q: 1. In three-space, find the intersection point of two lines ₁ = (−1,1,3) + t(1,2,-2) and r₂ = (5,3,…

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Q: -5 y 30 20 10 f 5 (5,2) 10 15 20 X

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