Find the area bounded by y = x + 4 and y = x² - 2. Answer:

Q: Consider the function f(x) = 9x° + 9x® – 6xª – 5. - 5. - Enter an antiderivative of f(x). Do not…

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Q: Q1/ Solve the initial value problem (IVP) of the differential equation by using the appropriate…

A: Initial value problem: An initial value problem (IVP) in multivariable calculus is an ordinary…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: 2. f(x)= 7x2 -19x - 6 at (4, 8)

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Problem 4: Use theorems on limits (limit laws) EXCEPT for the polynomial function rule, to get the…

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Q: How do you solve related rate problems in calculus? List all steps.

A: Step to solve rate related problems in calculus

Q: Solve for y in the following system of equations: x – y = -7 2x + y = -17 -8 О -1 O -3 O O

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Q: 8 of 22 If č = (-3, –5) and d = (-2, –6), find |47 – 2.5d|. V74 O 8/6 O 7/5 146

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Q: Find the area of the region. See Examples 1, 2, 3, and 4. f(x) = -x + 7 6. g(x) = = y 81 6 2 bo 2.

A: We can find the area under the curves as below.

Q: 12

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Q: If f(w) (3w), find f'(w). Use exact values. = COS f'(w) =

A: We can find the exact answer as below.

Q: Find the first derivative of the following functions Y = x5 e-3 ln x and Y = ln √ [ (x – 1 ) / ( x…

A: Solution is given below:

Q: 5y² = 2x³ – 5y

A: Derivative with respect to x

Q: Use an appropriate test to determine whether the following series converges. 7 Σ 3 k =1 VK

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Q: 3x + 1 Consider the function f(x) Compute each of the following. Simplify your answer and use x - 3…

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Q: Evaluate the integral. 2 dt 1- t2 V

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Q: 5. Find the Maclaurin series for f(x) = In(1 Do not use the building block from the previous…

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Q: Find the derivative of the function. 4 - 4x – x2 f(x) x2 - 6 — 4х — 2 - -1+ f'(x) = -x – 6

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Q: and the net is decribed by the equation y = V1 – x2 – z2, y 2 0,

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Q: IV. On Circular Permutation In how many ways can eight people be seated at a round table? . In how…

A: Note that, in a Circular fashion we can arrange n elements in (n-1)! ways.

Q: Determine whether the series is convergent or divergent by expressing s, as a telescoping sum. 00 n2…

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Q: 2x)y'+5y=

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Q: S 2x(ex²+1 – 2x*) dx

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Q: 27. In how many ways can each of the following be drawn from a standard deck of 52 cards? three…

A: As per guidelines we can solve only first three sub part of the question. Solution From a standard…

Q: Solve the two items using Integration by parts. 1. [x' V9- x² dx 2. Te2* sin x dx

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Q: Lety = 4x² – 4x+3 (a) Find the equation of the tangent line to the graph of the function atX=2; (b)…

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Q: Find the equation of the circle shown Ih

A: Three point  ( 0 , 4 ) , ( 0 , 2 ) and ( -2 , 0 )   equation of circle   From the graph  center ( h…

Q: Se2x sec?e2x Vtan e2x + 2 dx

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Q: Solve the differential equations: (a) = 4x+2x+5 where V(1) = 10 .

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: y-axis Consider the graph shown to the right 4. lim f(x) X-axis 5. Evaluate lim f(x) X-3 6. lim f(x)…

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Q: Use partial fractions to find the sum Σ (2n- 1)(2n+ 1) n = 1

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Q: 3. Let the statements A, B be A: (not p) and q, B: (not p) or (not q). If p 0 and q = 1, then !! %3D…

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Q: Y1 = x? Y2 = x3

A: Given

Q: 13. Use the Intermediate Value Theorem to show that f(x) = 2x° – 3 has a zero in the interval [1,2].…

A: Given:-f(x)=2x3-3 using the intermediate value theoremf(x) is continuous in the interval 1,…

Q: An advertising agency spends £x on a newspaper campaign and a further £y promoting its client's…

A: The Multiplier Method of Lagrange We may need to maximize (minimize) a function that is constrained…

Q: How do you do optimization in calculus? List all steps

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Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: We have been provided with 10 points in a plane such that no three points are collinear.We need to…

Q: 14. If a baby is dropped from a height of 300 meters, its height s at time t is given by s(t) =…

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Q: Find E( +1)? O 367 418 O 423

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Q: What is the slope of the tangent to the curve y=arctan 4x at x= 1/4 A. -2 B. 0 C. 1/2 D. 2…

A: To find the slope of tangent to the given curve.

Q: -1 Let f(x) = (3 sin z + 4 cos z)tan f'(x) = %3D

A: Given  f(x)=(3sinx+4cosx)tan-1xTo find f'(x):

Q: Given that f(x) = a°h(x) h( – 1) = 3 h'( – 1) = 6 Calculate f'(- 1). Hint: Use the product rule and…

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Q: Find the volume of the solid obtained by rotating the region bounded by the curves y = x°, y = 1

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Q: Find g'cx) gon= XX dx

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Q: 1 7. (x dy – y dx) = 0 x² + y?

A: We are given a differential equation  1/(x2+y2) ×(xdy - ydx ) =0 We have to determine whether it is…

Q: Find the nine roots of -256 – j256/3.

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Q: A physical education teacher found that 62% of the students exceeded the minimum standards. Which…

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Q: Given the equation 2x + 3y = 6, a second equation that forms a system with no solution is: O 2x – 3y…

A: Given; 2x+3y=6

Q: Determinant of 2 x 2 Matrices. Solve for the determinant of the following matrices: 7. 1. A = 4 6. 4…

A: 1.A=7-346 det(A)=7×6-(-3)×4=42+12=54 2.B=4-5-19 det(B)=4×9-(-5)×(-1)=36-5=31 3.C=213-312-27…