Find the average value over the given interval. -X. y = 5 e [0,4] The average value is

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A: To find the volume ..

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A: Given series is alternating is convergent

Q: Use the given information to find f '(8). f(x) = g(x)h(x) g(8) = 5 and g'(8) = 1 h(8) = -7 and h'(8)…

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 9…

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Q: Find the length of r(t)=[e"(cosbt), ea"(sinbt)] from t=0 to %=D1 (a and b are constants). This plane…

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Q: f(x, y) = xy over the triangular region with vertices (0, 0), (8, 0), and (0, 6) O 12 2 96 O 16

A: Solve

Q: Find the equation of the tangent line to the curve y = x Vx +5 at the point (2,6).

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Q: 7. Without using technology, solve the equation: log(x + 10) – log(x - 5) = 2 %3D

A: The given equation is: log (x+10)-log(x-5)=2

Q: 14. (a) For the angle Name the quadrant the angle lies in and its reference angle/number (b) Convert…

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Q: Let F(x) = f(f(xæ)) and G(x) = (F(x))² . You also know that f(9) = 3, f(3) = 2, f'(3) = 5, f'(9) =…

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Q: Expand each function (using the appropriate technique/formula). Compute the derivative of the…

A: "Since you have asked multiple questions, we will solve the first question for you if you want any…

Q: Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the…

A: The given sum,   1+8+27+64+125+216

Q: Find u - v, 2(u + 3v), and 2v - u. u = (4, 0, -8, 6), v= (0, 2, 6, 4) (a) u - v - (b) 2(u + 3v) (c)…

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Q: 3 f(x) =x° – cos(x) Solve this question by the Fixed-point method on the topic of solution of…

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Q: J (금2 + 3z2 +1) dz 4. 6) dx 5.

A: 4) the integration of the integral is 3z4/4 +3z2+1 5) the integration of the integral is  -2x5/3 -6.

Q: f(x) -? The graph of a function f and its tangent line at 0 are shown. What is the value of lim x→0…

A: Given query is to find the limit of the expression.

Q: Antiderivatives resulting in inverse trigonometric function secx tanx -dx J 9+ 4sec²x

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Q: The function I (t) = - 0.2t3 + 3t2 +100  for 0 ≤ t ≤ 9 gives the CPI of an economy, where t = 0…

A: This question can be solved by applying the relation between CPI  and inflation rate.

Q: Find the taylor series generated by f at x = a f(x) =3^(x), a=2

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Q: Write an equation of a rational function, in general form, which satisfies the following conditions:…

A: This is a problem related to function calculator. Based on the general concept we will answer the…

Q: * f(x) = x —х+ sin(x) — 1 Solve this question by the Bisection method on the topic of solution of

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Q: Graphs of f(x) (solid) and g(x) (dashed) are given below. Use them to find the following ives. Show…

A: Graph of  the function f(x) and g(x) are given, we have to find the value of h'(1)

Q: The side lengths of a triangular park are 11 yards, 13 yards, and 16 yards. What is the area of the…

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Q: Find the limit of the V4n +9 sequence lim Show your work. n- 00 9 n+4 Determine whether the (- 1)…

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Q: Sin 5

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Q: Determine the open intervals on which the graph s concave upward or concave downward. (Enter your…

A: Solved below

Q: A circular swimming pool has a diameter of 20 ft, the sides are 5 ft high, and the depth of the…

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Q: Find the integral (o (b+1)x*2 +(c+1))(x*** +(-1)"(a+2)) dx . b+2c+1 Vx°

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Q: on enclosed by 4+x ア= Find the area of 4

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Q: Find the area of the region bounded by the given curves (a) using integration with respect to x and…

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Q: "roblem #5: Use the divergence theorem to find the outward flux F.n dS of the vector field F =…

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Q: Determine whether the integral is convergent or divergent. 4 dz z2 + 6z + 5 convergent O divergent…

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Q: n²+n+1 En=1 n4+n² 00

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Q: What is the exact value of sin(67.5°)cos(22.5°)?

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Q: Answer all questions in the space provided. Show ALL your steps in your calculations. Answer in…

A: A function is defined by fx=x3+ax2+bx+1. To determine the values of the constants a and b such that…

Q: 4 dx x2 4x2 - -- x2

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Q: Determine the equation of the plane containing the point and the line. (-7, 10, —3), r(t) — (1 — 4г,…

A: To find the equation of the plane passing through the point (-7,10,-3) and containing the line…

Q: A firm wishes to distribute its total production between two manufacturing plants A and B. A contour…

A: To estimate the total cost of production from the given contour plots.

Q: 67 |xsin 3xsin 2xdx

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Q: |r sec? 3rdx

A: Here we have to solve the integration by using integration by

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Q: How much work is done by gravity in causing a 45-kg rock to tumble 54 m down a slope at an angle of…

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Q: Given two functions h(t) and g(t), is h¯1g-1 (t) = (hg)-1(t).

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Q: 10. For the function f (x) = -2· e* + 6, find the domain, range, and equation of the asymptote.

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Q: sec?x - dx |1- 4tan²x 1 –

A: We will solve this question using simple Integration formulae.

Q: USE THE LIMIT DEFINITION OF DERIVATIVE:  A wire 10 cm long is cut into two pieces, one of length ?…

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Q: The function P(t) = t² (2t + 3)5, can ONLY be differentiated by using the product rule. %3D Select…

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Q: For the following system of linear equations, one equation has been omitted from the syste 2h + 4n +…

A: Find your answer below

Q: Let a and b be real numbers. What integral must appear in place of the question mark "?" to make the…

A: Given query is to find the missing integral part.

Q: 10. Evaluate the following integrals (a) L x²+1 (b) J 군TT 1 x2 –6x+13' d.x

A: