4. Evaluate the following derivatives and definite integrals. (») & [[ ²³ d] = et² dt dr (b) La[+] dt -2 dt (c) / [[*cos(1³¹) dt] = dr I

Q: 2. Let g(x) = f(t) dt where f is graphed below. 3+ * 1 5 -1 3- 1 -1- (a) Find g(-1), g(0), g(1),…

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Q: dR 22 dt 3 R(1) 56

A: To find the particular antiderivative of the following derivative that satisfies the given…

Q: 40. Toys Belkis is pulling a toy by exerting a force of 1.5 newtons on a string attached to the toy.…

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Q: Compute the average value of f(x): = Average value = X 1 4x + 3 on the interval [2,6].

A: Given query is to find the average value of the function.

Q: 6.2 If 20% of x equals 7, what is x?

A: Solve the following

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A: Let's find flux across S.

Q: Evaluate. Use a capital C for any constant. [(6x (6x +4)7 dx =

A: To solve the given indefinite integral.

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A: The given functions, 1. y=2sin3x 2. y=5cos34x 3. y=3cos2x We have to find its period, amplitude and…

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A: To find the volume of a pyramid with a height of 16 and a rectangular base with dimensions 3 and…

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A: Given query is to find differential at indicated points.

Q: 6.7 Find the unique number which is equal to its half plus 1.

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Q: Consider f(x) = |x − 3| on [0, 5]. Find all c so that f(c) = fave where fave is the average value of…

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Q: Use the Fundamental Theorem to evaluate the definite integral exactly. So -0.1t e dt =

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Q: A cylindrical soup can has a diameter of 3 in. and is 4.7 in. tall. Find the volume of the ca in.3…

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Q: Use the Fundamental Theorem to evaluate the definite integral exactly. 1," 16 5 Enter the exact…

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Q: Find the surface area and the volume of each figure. Give the exact answers and the approximations…

A: We can find the surface area and the volume in the below steps.

Q: √3-4

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Q: Write an equation for the following conic section A parabola with focus at (-3,2), directrix x = 1

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Q: Find the domain of f . (Enter your answer using interval notation.)

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Q: b) Find a function f(x) such that both f′(x) = cos(x) + e^2x + 2x and the tangent line to f(x) at x…

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Q: 12. Evaluate the line integral rey ds where C is the line segment from (2,0) to (5.4)

A: We have to evaluate the given line integral.

Q: A metal cube dissolves in acid such that an edge of the cube decreases by 0.80 ​mm/min. How fast is…

A: given data  edge of the cube decreases by dldt=-0.80 ​mm/min instantaneous length of edge (l)=8.90…

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Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval and find…

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Q: b) Find a function f(x) such that both f′(x) = cos(x) + e^2x + 2x and the tangent line to f(x) at x…

A: Let's find function f(x).

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Q: Classify the following as a linear relationship, exponential relationship, or neither. Explain your…

A: We need to determine relation.

Q: Siven y=√x. Find dt = dx dt when y = 7 and (Simplify your answer.) dy dt = 1.55.

A: Given query is to find indicated derivative.

Q: (a) If g(x) = 2x + 2 and h(x) = 4x2 + 8x + 9, find a function f such that fo g = h. (Think about…

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Q: 4. When the infinite series converges, what does it seem to converge to?

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Q: (1-3p)² p4 .dp

A: Solve the integral

Q: A circle has a radius of 5 cm. If the radius is increased by 0.1 mm.. what is the estimated increase…

A: Given query is to find the Increase in area.

Q: Evaluate. 5 -1 -1 (4x²-3x+5) dx (4x²-3x+5) dx = (Type an exact answer in simplified form.) ***

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Q: Find an antiderivative of 7 z4–9 z6 27 Antiderivative = in the variable where x > 0. Remember to…

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Q: Given the information below, estimate the total distance travelled during these 6 seconds using a…

A: We need to perform left endpoint approximation.

Q: Express the number as a ratio of integers. 3.805 3.805805805...

A: Given 3.805¯

Q: Let x and y be two positive numbers whose sum is 175. Determine the values of x and y such that (x +…

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Q: Find the exact value of each expression. (Enter your answer in radians.) (a) sin-1 5-1 (1/²) 2 (b)…

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Q: Compute the Taylor series of the function around x = 1. f(x) = (x − 3)2 f(x) =   please show step…

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Q: 60. a. Find the linear approximating polynomial for the following function centered at a. b. Find…

A: Given that , fx=16x32 and a=9

Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A: dxndx=nxn-1f(x)=5x2+4for critical points put f'(x)=0

Q: 8. g(x) = n(1+t²)dt 12. R(y) = t³ sin(t)dt

A: To find the derivative of the following functions.8 gx=∫1x ln1+t2 dt12 Ry=∫y2t3 sint dt

Q: Determine a vector equation for a line that goes through the following points: (-8, 7, 8) and (-10,…

A: Determine a vector equation for a line that goes through the following points: (-8, 7, 8) and (-10,…

Q: Find all the values of x such that the given series would converge. ∞ n=1 n!

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Q: = Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: 1. Sketch the graph of each function, labeling any intercepts with their coordinates and any…

A: Since you have asked multiple questions in a single request we would be answering only the first…

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Q: A flu is spreading at a rate of dn/dt = 180t-3t² where n is the number of people affected at any…

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