14. Use a suitable change of variables to determine the indefinite integral. fsin²xcos³ xdx (Hint: sin²x + cos²x = 1)

Q: Use linear approximation, i.e. the tangent line, to approximate √49.4 as follows: Let f(x)=√x. Find…

A: For function, f  the linear approximation at a is given by L(x)=f(a)+f'(a)(x-a)   ...............(1)…

Q: jw F(w). [a - acos (wr)] - A 1 Tjw jwF(W) = -2A (1-cos (WT)). Tjw jwF(W) = -2A (asin ² (WT)) Tjw How…

A: since we have a trigonometric identity:                                   cos(2θ) =1-2 sin2(θ)⇒ 2…

Q: The marginal cost for printing a paperback book at a small publishing company is c(p) = $0.016 per…

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Q: The function f(x)=√x² + 7x has an oblique asymptote y = mx + b at +∞. Find the values of m and b.…

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Q: 2. Let f(x) = 2x²-3x+1 ,x 0.5 Determine constants A and B such that is continuous for all values of…

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Q: Find the characteristic equation for the matrix 2 (13). and use it to compute M-¹. M

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Q: Using Trigonometric Substitution a substitution of x = 6 sin(theta) was used to solve an integral.…

A: trignometric substitution

Q: xydx + (x^2+y^2)dy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: Please see the below picture  detailed solution.

Q: Find x² - y²¹ lim (x,y) →(a,a) x² - y² O 2a O 2a² a² 00 DO

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Q: Determine if the expression is meaningful. If it is, state whether the expression represents a…

A: The expression is given by ∇×∇×F To determine: Whether the expression is a vector field or a vector…

Q: Question 1 Evaluate the integral and choose the correct answer. e ln x fethe 01+e O dx 2 01-e A…

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

A: This question is related to definite integration, we will solve it using given information.

Q: y" +1²y=0, 0<x< 1 2y (0) + y (0) = 0 y(1) 0

A: Please find the detailed answer in the image attached.

Q: Use the trapezoidal rule with n = 5to estimate √√√7+y³dy

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Q: Evaluate O 10 • 4 5 9 2z plny Մ » 0 -T ye dædy dz.

A: To evaluate the integral.

Q: Evaluate 4 R³ TR³ O TR³ O TR² 2π 0 R p² sin odpdøde.

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Q: f(2x. (2x + 6)5 dx 0 (2x+6)6+ C 2 H|M 3 12 (2x + 6)6 + C (2x + 6)6 + C (2x + 6)6 + C

A: A detailed solution is given below.

Q: For which of the following infinite series does the Ratio Test fail? IM8 IM8 k=0 k 5k そそ n=1 (n +…

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Q: Phyllis invested $9,500, a portion earning a simple interest rate of 8% per year and the rest…

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Q: Graph the function. What symmetries, if any, does the graph have? Specify the open intervals over…

A: The graph of a function f is symmetric about the origin if             f(-x) = -f(x)

Q: Example 1 Find dy/dx, if a. y=sin(x² + 3x + 1) b. y = cos² (2x-1)

A: I have stated the used formulas in the solution

Q: Σ η +1=2 In(n), π

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Q: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: [xcsc (y/x) - y]dx + xdy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: The given differential equation is; [xcsc (y/x) - y]dx + xdy = 0

Q: (c) Compute the principal unit normal vector N of r(t).

A: Given :  Unit tangent vector  T(t)=11+5t21,t,2t,    0≤t≤2 T(t)=11+5t2,t1+5t2,2t1+5t2,    0≤t≤2…

Q: cos^2(2x) - sin^2(2x)=0. Is it a identity and how can you tell.

A:

Q: √ √x dx W|N 3 x2 + N/W N/W + C + C 2/3 + C

A:

Q: Question Find the change in surface area dA if the radius of a sphere changes from 11 cm to 10.8 cm.…

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Q: Consider the function f(x) = 10√x + 4 on the interval [1, 8]. Find the average or mean slope of the…

A: Given the function is fx = 10x+4 on the interval 1, 8.

Q: QUESTION 15 Use a graphing utility to graph the function over the indicated interval and approximate…

A: The answer as follows:

Q: 3. Explain why lim √2x - 6 does not exist.

A: 3. The given limit is limx→32x-6 Note:    Multiple questions are given, we are answer with only one…

Q: Newton's Method will fail to approximate the solution to f(x) = 0 with initial guess to whe Of(x) is…

A: Given :Newton Method :xn+1=xn-fxnf'xn

Q: Show the complete solutions, kindly include all the necessary drawings, graphs and illustrations.…

A: We have to find the orthogonal trajectories of circle through the orgin with centre on the x axis

Q: How many different 9-digit phone numbers do not contain the digit 9? Assume that any digit in the…

A: Given data÷ How many different 9-digit phone numbers do not contain the digit 9. Assume that any…

Q: Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand…

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Q: A botanist is studying the development of a bamboo plant. She started keeping a log of its growth 25…

A: Total time= 25 weeks Given that the plant has grown an average of 35 inch each week.  So the plant…

Q: ∞ f(x) = L n=1 (7-2x)" Sn

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Q: If the population of a country is 100 million people and the population is increasing exponentially…

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: 6 A small resort is situated on an island off a part of the coast of Mexico that has a perfectly…

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 400+600t - 180t2, where t is…

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Q: Consider the function f(x) this interval. 1 on the interval [5, 11]. Find the average or mean slope…

A: Given, f(x)=1/x

Q: FT [f'lt) = jwF(W) F(w) = jw f(w) => JA -T T tax + √(-_^) -jut e (-A) ²-just, AT Sim ² (WI) WT T A […

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Q: Find the centroid of the region bounded by the graphs of the functions y = 5x², y = x² + 6 The…

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Q: The surfaces p = 3 and 5, p = 100° and 130°, and z = 3 and 4.5 identify a closed surface. (a) Find…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Find the exact value of the expressic ܪܕܐ -1 sin sin ၁ 5 သ | O 2n O 2n 5 5 Эт O 3n 5 3 5

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Q: Find the exact sum of the following series (0.25)" (0.25)³ Σ(-1)n-1 n 3 n=3 (0.25)4 4 + (0.25)5 _…..…

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Q: Problem 1 Solve the first order ODE with an initial condition y(1) = 2. Here yy(t) is the unknown…

A: Given first order ODE is y'+1ty=ty2 and its initial condition as y(1)=2 We need to find solution for…

Q: Find the general solution to the differential equation: y' = 8x + e²r

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Q: Given the demand function D(p) = √300-2p. Find the Elasticity of Demand at a price of $14 0 X

A: We can find elasticity of demand.