Note: Below we are using t as the variable for angles instead of 0. 1 Consider the following integral / dx VI+(5x – 4)2 To simplify the integral, the most appropriate trigonometric substitution is x = f(1) where f() =| After the substitution and simplification (trig identities), we obtain the integral / g(t) dt where g(1) =| This integral becomes the following function of t g(1) dt +C After substituting back for t in terms of x we obtain the following final form of the answer: +C

Q: Solve the differential equation Q1 y" - 3y' + 2y = 0 when y(0) = 1, y' (0) = 0 %3D %3D

A:

Q: Sections 4.1, 4.2 To receive full credit on this Homework assignment you must show all your work.…

A: We have to find value of given indefinite integral.

Q: If f(x) dx = (2x – 14)12 + C, find f(x). %3D f(x) %3D

A:

Q: 2. If f(x) and g(x) are continuous functions, then " g(x)] dx = | f(x)dx• g(x)dx. 3. If f(x) and…

A: Note :As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Let u=sinx and the integrand will lead to integration by partial fraction

A: use substitution method for solving the  integral

Q: Activity 4: Let F be functions defined by the following. Find their derivatives then list down three…

A:

Q: Y = 1 - x², y = 2 + 2x, and y = 2– 2x

A: Let's find.

Q: Suppose we know that the power series )an(x - 8)" converges for x = 4. What other values of x n=1…

A: we will use ratio test to check convergence of power series.

Q: 2) Vy + 2x = (e – 1)3

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

Q: 4. Evaluate y = sin¬1 (x) when x = 1 %3D O 37 2 -1

A:

Q: Given the triangle below, find the exact value for sec(@). 13 12

A:

Q: 2. What is the period of the graph below? O 4 O 2 O1 PREVIOUS 2 of 17

A: Given query is to find the period of the graph.

Q: Find the absolute maximum value of f(x) = x2 – 2x + 12 over the interval (0, 4]

A:

Q: An open topped box is to be made from a rectangular piece of metal 18cm x 48 cm by cutting off…

A:

Q: LIMITS 1. Evaluate the following limits, if they exist. If they do not exist, but approach too,…

A:

Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

A:

Q: 2) y = 3tan 3 - -2 3n 27 5n 3n 7 47 9n

A: Given query is to graph the function.

Q: find an equation of a cubic function if the graph has a y-intercept of 2, a stationary point at…

A: Consider a cubic function and satisfy the given conditions.

Q: Suppose that the marginal revenue from the sale of x units of a product is MR = R'(x) = 9e0.01x,…

A: Se integration for finding the revenue function.

Q: 24. Find the area of the triangle having vertices at (4, 5, 6), (4. 4, 5), and (3, 5, 5).

A:

Q: 26. Find a unit vector whose representations are perpendicular to the plane containing PQ and PR if…

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) (x2 + 2x – 2) dx…

A:

Q: xsin-1x dx V1-x2

A: We know, ∫udv=uv-∫u'vdv ddxsin-1x=11-x2

Q: 12. The graph below represents a periodic graph. y 5+ 10 12 14 16 4.

A: Topic = Functions TRUE

Q: Three slopes are given. For each slope, determine at which of the labeled points on the graph the…

A:

Q: 29. Find the volume of the parallelepiped PQRS if the vectors V(PQ). V(PR), and V(PS) are,…

A:

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 3 4 6 2 8 5 7 3 7 2 7 9. (a)…

A:

Q: The integral 5x – y dA = 59 if R R={(x,y): - 3<x<- 1, 5<y<6}

A:

Q: Find the absolute maximum value of f(x) = x? 2x + 12 over the interval [0, 4] -

A:

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = x2 + y2 + z2 (4,…

A:

Q: 17) x = In(9t), y =e9t, t>0

A:

Q: The value C for the solution of the initial value problem f'(x) = x - 8 +4, given that f(0) = 0. %3D…

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

Q: Evaluate the definite integral: 7/4 1+5 cos2 (t) dt cos? (t)

A:

Q: Given the triangle, find the angle 0 in radians. Round to the nearest tenth.

A: Given the triangle below, our aim is to find the value of angle θ in radians.

Q: 6.26. у - 3у %3D0

A:

Q: 3 The antiderivative of the function f(x) = + 9x is x2 -3 4.5x2 + c 3 + 18.0a? + c 6- + 1.5x + c 3 +…

A:

Q: Sxsin?xdx 2

A: ∫xsin2xdx sin2x = (1 -cos2x)/2 put this in equation ∫ x(1 -cos2x)dx/2 ∫ x/2dx - ∫ xcos2xdx/2 x2/4 -…

Q: 00 12x Find a power series for f(x) , ]x| < 1 in the form an. (x? + n=1 Hint: First, find the power…

A:

Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: Evalua fe the integral 7) Of xy dx sübjcct to the functional relation X = at and

A:

Q: Find the absolute maximum value of f(r)= x-2x+ 16 over the interval 0, 5

A:

Q: The entire graph of the function f is given below. Round your answer to the nearest integer, if…

A: Relative maxima is the largest point in interior of the domain.

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

A: Suppose the point (x,y) on the line x+y=3 is nearest to the point (0,0). That is distance d between…

Q: The value C for the solution of the initial value problem f'(x) = x³ – 7x + 3, given that f(0) = 0.…

A: Given problem:- The value C for the solution of the initial value problem f'(x) = x3 - 7x + 3, given…

Q: Write the equations in cylindrical coordinates. (a) 7x2 - 8x + 7y2 + z2 = 7 (b) z = 2x2 – 2y²

A: We have to find cylindrical form of the given equation.

Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

A:

Q: 6. S COSX dx sin2x

A: Solving the problem by finding the value of the integral.   NOTE :: As per our Expert guidelines we…

Q: Evaluate the tolloW ing limits と-1

A: =limx→1  x-1x2+x-2=limx→1  x-1x2+2x-x-2=limx→1  x-1x(x+2)-(x+2)=limx→1  x-1(x+2)(x-1)=limx→1…

Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: EXERCISE 1 Solve the following ODE from x = 0 to x = 1.0 using the Euler's method with the step size…

A: