if: z = cos 0+isin prove that: 1) 2+1 z+1 2)221 +1 = itan 0 z² = Z

Q: Describe the surface with cylindrical equation r=6

A: We have to describe the surface with cylindrical equation r=6.

Q: F. (DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS) 1. Find f'(x) if f(x) = 3e². 2. Find g'(x)…

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Q: Question 6 Find the indefinite integral below. (3³¹-5sin - 5 sin(5t)j +15cos(5t)k)dt Do not include…

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Q: 9. Solve the differential equation: xy + y'=100x

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Q: t dy dt a. Find y(40) b. Findt where y(t) = 900. 78. If = .08y (1 - y 1000) y(0) = 100

A: We need to find y(40) and t.

Q: D O 1.909 Question 14 Find the length of the plane curve given below. r(t) = 5cos(t)i+5 sin(t)j, [0,…

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Q: 30. Let f: RR and g: R → R be defined by f(x) = 3x + 1 and g(x) = x² - 2. Determine (fog)(2) and…

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Q: Find the general solution of the differential equation. y(4) + 2y″ + y = 7 + cos(2t). NOTE: Use C₁,…

A: To find the general solution of the given differential equation.

Q: Question 3 Find a vector-valued function, using the given parameter, to represent the intersection…

A: We need to find r(t).

Q: Differentiate implicitly to find dy/dx. ²+ y² - y² = 29 dy dx 11

A: This question is based on implicit differentiation.

Q: Part b: (**) We consider the function f(x, y) = x sin y - y cos x + y Find fx(x, y), fxy(x, y), and…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Consider the following function. f(x) = (x - 3)ex (a) Find the critical numbers of f. (Enter your…

A: We have to find the critical points, monotone intervals and relative extremum.

Q: An aquarium 7 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of…

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Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: The given function,   cosx+tanxy+4=3

Q: The straight line beams between the radar dish and the drone registers a distance of 32 km. What is…

A: Given: the triangle ABC in which there is 90 degree angle at A      Use: sin(θ)=…

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Q: Work Problems ( your works 1) Let F(t)=(4t — t²)i+t² j+sin(5t — 10) k - - - You need to show all a)…

A: Given: Ft=4t-t2 i+t2 j+ sin5t-10 k

Q: 7. Find the equation of a line tangent to the graph of f(x) = cotx at x = π/4. Show all steps to…

A: Given :fx=cotx

Q: urses/22237917assignments/25899809 Use Newton's method to approximate a root of the equation x³ + x…

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Q: Compute the determinant of the matrix by cofactor expansion. 325 114 O-56 -8 O110 8

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Q: Solve the following initial value problem: y(t) = = dy dt +0.9ty = 6t, y(0) = 1

A: Given: dydt+0.9ty=6t,      y0=1

Q: if :z = cos 0+isin 0 2z² z²+1 prove that: 1+itan 0

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Q: To evaluate the integral 1. 7 64 + x² -dx,

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Q: Evaluate the integrals using partial fraction 3y²-y+! S y³ - y² dy

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Q: Use the given acceleration function and initial conditions to find the position at time t = 1. a(t)…

A: (9)

Q: Find the solution of the given initial value problem 150y" + 25y"+y′ = 0, y(0) = −14, y′(0) = 10,…

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Q: Work problem 30 Given the vector function 5 F(1) = (61³ – ¾, sec(4 − 1)), t then find the tangent…

A: Given :Ft=<6t3-5t, sec4-t>at t=4

Q: Consider the indefinite integral fe5z +6 dæ: a) This can be transformed into a basic integral by…

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Q: Solve Problem 346 in section 4.7 of the textbook. In addition to providing the calculations, draw a…

A: Solution is given below:

Q: integral of cos x sin^3 2 x dx

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Q: Set up the definite integral required to find the area of the region between the graph of y = 13-²…

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Q: If f is a differentiable function and % up on Selected Answers: (0,1) f'(x)=x5 − 5x4+ 5x³+2, then…

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Q: Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of…

A: Here we use formula of sum of n term of geometric series.

Q: The result of the integral is equal to 4 √ = (x − 1)(x + 1) dx

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Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i3j-k, find vector normal to A and In plane of A and, B.…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first first question.…

Q: Aphelion Center Mean distance Peribelion + Sun Major axis Use the fact that the orbit of a planet…

A: We need to give equation of orbit.

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

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Q: If the first 5 terms of a geometric sequence are {12, 6, 3, the formula for the nth term in the…

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Q: Which of the following is dž for t = 1 if dz dt 2t Z = In(x²y³), x = e¹ and y = e²¹ ? Select one: O…

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Q: Use the implicit differentiation to find dy/dx. Then find the slope of the curve at the given point.…

A: By using the implicit differentiation to find dydx. Then to find the slope of the curve at the given…

Q: Given the function f(x, y)= xye+tan² esec2 y The second derivative fyy of f is equal to 0. Select…

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Q: Use the given information to find the exact value of the trigonometric function.  sin θ = 1/4 , tan…

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Q: Let f(x, y) = domain of f is the set D = {(x, y)|x² + y² > 1}. Select one: 1 1 - x² - y² True O…

A: Given.

Q: tan² (x) sec¹(x) dx.

A: Given, ∫tan2(x)sec4(x)dx

Q: E. (DERIVATIVES OF TRIGONOMETRIC FUNCTIONS) 1. If f(x) = secx + 3 csc r, then 2. If g(x) = x² sinx -…

A: To find the derivatives of the following functions.1 fx=sec x+3 csc x2 gx=x2 sin x-3x cos x+5 sin x

Q: Which of the rectangles below are both left and right rectangles? 10- 8- 6- 4- 2- 0- 0 8 CD 0000 05…

A: Rectangle which is both left and right rectangle is the rectangle which touches the function from…

Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: 3.745 O 7.491 Question 13 Find a at time t = 2 for the space curve r(t) = (8t − 7 )i+t²j− 10tk.…

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Q: 8. Use that (1+x)-2 = 1-2x+3x² - 4x³ + for -1 ≤ x ≤ 1 to find the first four nonzero terms of the…

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Q: Let F(x) = = (x − 3)³ − 4 cos (x-3) Find lim F(x). x 3 + lim F(x) = x+3+ x < 3 3 ≤ x

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