Show all necessary solutions. I. Find the equations of the horizontal and vertical Tangents. a. 25x? + 200x + 16y² – 160y + 400 = 0 b. x3 + 3x2 – y2 = 0

Q: 3. Write z = 12.2 - 31 in polar form. Use 3 decimal places.

A: The objective of the question is converting to polar form.

Q: 9. Verify the identity 1 1 = 2 sec² x 1-sinx 1+sin x

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Q: VI. Use Lagrange Multipliers to solve the following: Maximize f(r, y, ) = 4x + 2y +z subject to z +…

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Q: Step 1 To find the definite Integral 9 dx by the limit definition, divide the Interval [2, 7] Into n…

A: For the asked steps we can solve as follows.

Q: f (x)= arcsin (x³)+ aretan (4x)

A: derivative

Q: 16X

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Select all that apply. Select the functions whose value is zero. sec 270° Csc 360° tan 90° cos 270°…

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Q: dr 1/4( In 4) o 1/( In 4) o In 4 In (4) 1/4

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Q: Evaluate the integral -2x + 4 dx J (x² + 1)(x – 1) 2

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Q: For the following function f(x), find f(0) and f(2). if xs0 x2 f(x) = if 0 <x<2 x+3 if 2sxs4 4-x…

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Q: d Calculate ri(t) · r2(t)] and d ri(t) x r2(t)] first by differentiating dt' dt the product directly…

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Q: The integral of the given function sin³x cos x dx is equal to а. 1/3 b. 1/4 с. 1/5 d. 1/6 e. None of…

A: To evaluate: I=∫0π2sin3x cos x dx

Q: Eliminate the arbitrary constant on the given equation: y= G1r + C2e O (2? 22) y"+ (2 + 2) y- (2 2)…

A: The given equation is y=C1x2+C2e-x. We have to eliminate the arbitrary constant C1, C2.…

Q: Which of the system of equation has no solution? 2х - 4y%3D 4 – 3x + 6y = – 9 а. С. X— 2у %3D 3 | 3x…

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Q: how does csc x/ cos x is equal to sec^2 x/ tan x

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Q: If f(x) dr = 6 ,what is the value of f(5 – 1) dr

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Q: If f(z) = 4,/ In(x), find f'(x). Find f'(2).

A: Given function:fx=4xlnxWe need to find f'x and f'2.We will use the following…

Q: Exercise 2. Find the following limits 3x +1 1-3x² 3x +1 1) lim to 2x + 5 2) lim X+ 2x +5 3) lim x-…

A: Use limit concept

Q: Find the equation of the tangent line at the given point on the curve. 327x 3x² + 3y² , 109y 2 10…

A: As we know that; The expression for the equation of the tangent line is: y-y1=mx-x1 Where, m is the…

Q: 8. The rationalizing substitutionw + 4 = u² transforms - dw into w+4 A. fu² - 4°du B. 2fu² - 4}du C.…

A: Given: I=∫w2w+4dw  ...1   As we know that; The Power law: ddxxn=nxn-1 And ∫a·fxdx=a·∫fxdx , where a…

Q: dy 3) y = u5 and u = 3x – 1; 2 Ans: 2 = 15(3x – 1)* %3D dx dx

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Q: Which of the following DE has separable variables? O (xy? + x)dx + (x²y-y)dy=D0 O (x- y)dx+(3x+…

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Q: P1:

A: Solving

Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + 2y + = subject to x2 + y…

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Q: Find the following using the table below. 123 4 f(x) f'(x) | 3 | 1 | 4 2 2 3 4 1 (x)6 2 3 4 1 E|…

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Q: Differentiate y = sin¬' (sec(4x²)) A. 8x tan(4x²) sec(4x²) y' V1 - sec2 4x² В. 8x tan(4x²) sec(4x²)…

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

Q: dx (x² + 1)

A: To solve the given integral

Q: 24. (EXERCISE) Consider the function f(x)=3x* – 20x' + 42x² – 36x

A: The given function,   f(x)=3x4-20x3+42x2-36x

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A: Explanation of the answer is as follows

Q: 1 is convergent or 1) Use the Integral Test to determine whether the series divergent. ' (3n– 1)?…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

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Q: Explain why the function f(x) = ez is not injective (one-to-one) on its natural domain.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: The equation x² + y2 = 25 has O a center at (0, 0) and a radius with a length of five units. O a…

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Q: k. f(x)=cosh(x³)+ sinh(10x) 1. f(x)=In(x* +1)

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Q: Use the chain rule to find the derivative of 16 f(2) = 2(– 3x0 – 52)" You do not need to expand out…

A: Given: f(x)=2-3x10-5x916

Q: 10. Find the area bounded by 2. Hhe curves y=8x-x²0ind y=3x

A: topic - area bounded by curves

Q: The position of a point at time t = 1 is (2, 4) and velocity of the point at time t is . Wha the…

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Q: Еxample 5 1 1- Vxdx ха 0,

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Q: csch 3x – 5 [3х — 10. dx V3x – 5

A: 10) To evaluate: I=∫csch43x-53x-5dx Substitute 3x-5=u⇒123x-5(3) dx=du⇒13x-5dx=2du3 ⇒I=∫csch4u2du3…

Q: etermine whether f is continuous at c= 0. - 3x if x #0 f(x) 2 x* + 3x %3D if x = 0 f continuous at…

A: Topic:- function

Q: A cube 3 inches on an edge is given a protective coating 0.1 inch thick. About how much coating…

A: solution:-edge of cube=3 inchescoating=0.1total edge length of cube with coating=3+20.1=3.2…

Q: The equation o=- in spherical coordinates represents sphere. Select one: True O False

A: Here, the given equation is: φ=π5

Q: 2. Evaluate the following definite integral. You can assume the function is defined b the limits of…

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Q: 2) z= (1+t²)(3 - 2y); z' Ans: z' = -2(3t? + 3t + 1)

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Q: Solve the second derivative(y") of the following

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Q: 6- Give ā = [A, B]and b = [F,E], find VProj(b onto ā) and SProjd onto b). Resolve d into…

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Q: Find the volume by revolving the region of the curve xy = 6 from x = 2 to x = 4 about the x-axis.

A: Given xy=6        x=2 to x=4To find volume:

Q: (a) Explain why the function f(x) = e is not injective (one-to-one) on its natural domain. (b) Find…

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Q: exdll Values of the six trigonometric functions of the angle. (-7, -4) sin 8 =-0.496 cos e =-0.868…

A: Find your answer below

Q: 3 1 - dx 2 2. cos sin X

A: solution:-∫cos4xsin3x1x2 dxlet 1x=t-1x2dx=dt=-∫cos4tsin3t dtWe know that the formula  2cosAsinB =…