Consider the function f(t) = 3 sec²(t) - 3t². Let F(t) be the antiderivative of f(t) with F(0) = 0. Then F(t)-

Q: Approximate the area under the curve y = x from x= x³ with 6 subdivisions. = 2 to 5 using a Right…

A: The curve y=x3 from x=2 to x=5 we have to find the area under the curve using Right Endpoint…

Q: 3. Find the domain of f(x) = = 1 - 1- x X

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Q: Find the average value fave of f(x) = x5 between -1 and 1, then find a number c in [-1,1] where f(c)…

A: We have to find the average value of function and value of c.

Q: If [ 2013 |檳 sin ada = −a³ cos x + 3x² sin x + k fæ sin ædæ, find k d. 3/2 a. 6 b. -3/2 C. -6

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Q: Find the area of the region enclosed by y = 6x² and y = x² + 1. Round your answer to three decima…

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Q: True/False: Answer a) for True, b) for false and mark on the scantron. 24. The following is a…

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Q: The infinite series Σ a. series liner 8 n¯4 is a

A: We know that the p-series is the following. Thus, for             p=4.

Q: The class outing ticket includes a snack-pack with three items, a cooldrink, chocolate and then…

A: Given tree diagram shows all the possible combination of "cooldrinks", "chocolates" and "chips or…

Q: Which one of the following equations could work for the following graph? y = 5 y = -5…

A: To find,  the equations could work for the given graph.

Q: Which of the following equations describes the nth term for the sequence O (3) -1(9)*** 4 1 1 1…

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Q: Find the antiderivative F(x) that satisfies the given condition: f(x) = 4x² +5e"; F(0) = -2. Show…

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Q: Explain the steps you would take to find the derivative of f(x) = (-)e -3x+tan(3x-5)

A: Given: f(x)=12e-3x2+tan(3x-5)

Q: Given R = = [² (³ + + ²) - (² + 4)] i n n a= So integral, that is provide a, b and f(x) in the…

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Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: f(x, y) = x4 + 13x³y³ - 5xy4 + 14

A: Given: fx, y=x4+13x3y3-5xy4+14To Find: To determine ∂f∂x and ∂f∂y.

Q: Use the rules for sums of powers of integers to compute the sum. 21 Σ; j=5

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Q: Determine for the following function: dy dx y = log3 (x² + 1) ○ (z²+1) In 3 2x O (1²+1) 2x O 2x…

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Q: For the curve: f(x)=√x-5 the equation of the tangent line when x=9 is Oy--(x+1) Oy--1(x-1) y= Oy- (x…

A: This question can be solved using the concept of tangent and normal.

Q: 5) Integrate 2x cos (x²-5) with respect to x.

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Q: The graph shows the rational function f (x) and the logarithmic function g(x). f(x)…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: 7. y - y = 16

A: The objective is to find the general solution .

Q: 1.4 1.5 1.6 Calculate if there is a surplus or deficit after the class outing. What percentage of…

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Q: Onsider the function f(x) = -4x²+7x+6. Interpret the e average rate of change from x = -7 to x = 7…

A: Topic:- application of calculus        Definition :-  The tangent represents the instantaneous rate…

Q: Find the surface area of the portion of the cone x² + y² = z² above the region inside the…

A: Let's find surface area of the cone.

Q: 5 S³ƒ( en that wer= f(x)dx 10 3 is ['f f(r)dr? what is

A: Topic :- application of integration

Q: •+∞0 4-1² 1 x² + 4x² dx

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Q: OC Find the derivative of the function y = dy dx dy 8 dx dy dx dy = - 8 x-4/5 ∞ 188 5 8 x-2/5 x 5²…

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Q: Using the Factor Theorem, which polynomial function has the zeros 5 and 4-5/? Ox²-9x-5x + 25/+20…

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Q: Find the volume of the solid obtained by rotating the region A in the figure about x = −3. b y 0 A…

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Q: II. Given a piecewise function f(x) = 2. 2x² + 2x " X log₂ (x − 1), x<-2 −2 < x < 2, x‡0 x ≥ 2. 1.…

A: The given piecewise function, fx=2,x&lt;-22x2+2xx,-2&lt;x&lt;2, x≠0log2x-1,x≥2

Q: Set-up the double integral that will solve for the volume of the solid in the first octant bounded…

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Q: Proor: Let † and g be one-to-one functions. a) Prove that (a) fog is one-to-one b) Prove that (b) (ƒ…

A: We will prove this using the concept of one to on

Q: 2. Approximate v1.02 +0.02 using an function f(x)=√x + 1 + e*. appropriate local linear…

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Q: What is the explicit equation for the nth term of the arithmetic sequence 6, 3.5, 1,-1.5, 4,...?…

A: We have: a1=6 -- the first term   Next, we calculate the common difference d=a2-a1 So, we have:…

Q: = 5. Prove the identity: cot(A + B) cot(A − B) = cot² B tan² A tan² A cot² B-1

A: To prove cotA+BcotA-B=cot2B-tan2Atan2Acot2B-1

Q: Evaluate d2y/dx2 at the point (0, -9). x = t3 - 3t y = 3t2 - 9

A: Given: x = t3 - 3t y = 3t2 - 9

Q: Suppose that a particle moves along a straight line with velocity v(t) = 14 - 6t, where 0 < t < 1.5…

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Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: 3. Find the domain of f(x) = 1- 1 X X

A: We have to find the domain of f(x)

Q: An object moves with velocity as given in the graph below (in ft/se How far did the object travel…

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Q: Given f''(x) = ¹ƒ(7) Find f [ 16 sin(4x) and f'(0) = 0 and f(0) = 1.

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Q: Find the average rate of change of f(x)=ln(x)fx=lnx over the interval [20.25,39.5].20.25,39.5. Round…

A: The average rate of change of f(x)=ln(x) over the interval [20.25,39.5]

Q: -3x²+tan(3x-5) Explain the steps you would take to find the derivative of f(x) = (e

A: Our Aim is to find the derivative of f(x)=12e-3x2+tan3x-5 -(i)

Q: Solve the area bounded by the curve y = 4x-x and the lines x=-2 and y = 4. 12) Sketch of the curves:…

A: The given problem is solved below in detail.

Q: The route that a trolley takes around a city can be represented by the functions x² + y² = 5. A…

A: To find out the location means the points where the trolley meet the train.

Q: Evaluate the following limit: lim 2²-25 x→2 2-5 O Does not exist. 0-7 07

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Q: For which one of the following lines would the graph fall exactly on top of the x-axis? x = 0 y =…

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Q: What makes solving inequalities different from solving an equation with an equal sign? For an…

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Q: Find the total surface area and volume of the solid object shown to the right. Use the key for s The…

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