Use the following equation to answer the questions: y = 4 cos (1/₂) 4 Find the period Find the amplitude Graph the function below. Choose the left button. Plot your starting point at the amplitude, then one more at the next amplitude. 6- 5- 4- 3 2 1 -8± -7ā -6ā -5n -4n -3n -2n - _] T 2π 3π 4π 5π бл 7л 8π -2 -3

Q: /5 too dr Vx-1

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Q: The statement (A + B) - (C' n B) = (A + C) is an identity. (Hint: draw a Venn diagram of the LHS and…

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: Date Jan 16 Feb 16 Mar 16 Apr 16 May 16 Jun 16 Hours light 8.95 10.18 11.62 13.27 14.65  15.40…

A: Month       Day light hours value Let say, the function is : y = asinbx-c+d

Q: Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y +3…

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Q: y = x4 - 8x² + 8

A: Here we have to sketch the function y=x4-8x2+8 ............................................ (1)…

Q: Find the intervals where the function f(x) = 2cosx + 1/ sin2x, 0≤x≤ 2π is concave up.

A: Let's solve.

Q: 5. Determine the area below f(x) = 10 - 2x² and above the line y = 3. 6. Determine the area bounded…

A: Given problem:- Determine the area below f(x) = 10 - 2x2 and above the line y = 3

Q: In the following table the values series y are consecutive terms of a series which the number 31 is…

A: Concept: Newtons forward difference interpolation method: Extrapolation is the process of computing…

Q: Evaluate the integral dx fax √2x-x1

A: Given: I=∫dx2x-x2   As we know the common integral; ∫11-x2dx=sin-1x+C

Q: Solve the following definite integral problems 1. Determine the area below f(x) = 8x - 2x² and above…

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Q: Q2/ Examine the following surface for maximum, minimum, and saddle points 2 = x² + y² + xy + 4x - 4y…

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Q: Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 8x² +17x - 10 on the interval…

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Q: Find the derivative (df/dx) 1- f(x) = cscx - 4√x + 7y-² 2-f(x)=x² cotx-x-2 3-f(x) = (secx + tanx)…

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

Q: 6x² - 2x - 1 4x³ X jo dx

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Q: Answer the given problems in two ways: (1) by using Chain Rule (2) by finding f(g(x)), taking the…

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Q: Solve the given differential equations: X 2. y' = , y(0) = -2 y+x²y

A: To solve the given differential equation.y'=xy+x2y, y0=-2

Q: d dx [47 tot 1 3x17 5 13 + 10 L 25 +100

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: 2. Show that the function. 5x²³²Bin 12 F(x)= โ x2 0 (x=0) is not of bounded variation on [1,1].…

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Q: Transform the given system of differential equations into an equivalent system of first-order…

A: Given

Q: Q4/ A/If x² (y - 4z) - y²(2x + 3z) + z²(3x - 4y) = xyz Find Zx

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Which of the following is correct in solving 3/22 2x√2 + x dx? Trigonometric substitution can be…

A: To determine which of the following is correct in solving ∫2x2+x dx.1 Trigonometric substitution can…

Q: = [ (23a)" e1¹0z da, Consider the integral n is a natural number greater than 1, When applying…

A: Given problem:- J = ∫ (23x)n e10x dx

Q: 9. Find inverse Laplace: 1 es S

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Q: Consider the improper integral and the propositions dx J = = 6of foo x² + 3 1- The integral J…

A: Find out the correct statement.

Q: (Simplify your answer.)

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Q: ind the equation the tangent line and normal line to the graph of f(x) = x³ at x = 2.

A: Given f(x)=x3 substitute x=2 in f(x)⇒f(2)=23=8 The tangent line passes through the point (2,8)…

Q: Write the relations and convert polar to Cartesian coordinates of ( 1, 45° ), then draw the point…

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Q: 1) In the triangle that determined by the points P.Q and R, find a unite vector perpendicular to…

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Q: 1. By using the method of variation of parameters, solve the following differential equation d²y +9y…

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Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: Which of the following gives the area of the region bounded below by y = sin(x), above by y =…

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Q: For the piecewise function f graphed below, find the following. y-axis 6 5 4 3 2 1 78 9 10 11 12 13…

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

Q: g. The line through (0.-7,0) perpendicular to the plane x+2y+2z=13 h. The line through (2,3,0)…

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Q: In the Figure 1, if Q= 40 N, R = 100 N, and B = 145°, then C is equal to: Figure 1: с A R B P

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Q: Evaluate the following integral. r/4 1 (s secx- cos cos sx)²dx 0 x/4 ļ (secx- cos x)²dx= 5 3 4 8 0…

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Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

A: We have to find the solution of given D. E.

Q: QuIf w=f(u, v) = cos uv, u = xyz ,v= 4(x²+y²) dw Prove that = 0 at the this point (x,y,z)=(1,1,1) дх

A: Given : w=f(u,v)=cos uv   , u=xyz ,v=54(x2+y2)   To Prove: ∂w∂x=0   at (x,y,z)=(1,1,1)

Q: 5. lim, A.7 Oi O о O. +D T 7x²+x-100 2x²-5x B 712 NIT D.2

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Q: Use the graph to identify absolute maximum and absolute minimum values for the function on the given…

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Q: B3. Find the integrating factor by inspection then solve.  ydx + (x + x4y2)dy = 0

A: Let's solve given diffrential equation.

Q: Use Lagrange multipliers to find the shortest distance, d, from the point (1, 0, -2) to the plane x…

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Q: Prakash is on a hiking trip. On the first section of the hike, he walks 5 km from the Hawk Campsite…

A: Given that Prakash walks 5 km from Hawk campsite(A) to the Condor Campsite(B).  Then, he turns and…

Q: a) Using the methods of equations. 2x+2y + 4z = 18 x+3y+2z=13 3x+y+3z=14 (b) Gauss-Jordan, solve the…

A: Given :2x+2y+4z=18x+3y+2z=133x+y+3z=14

Q: Suppose F(x) = f(x² + 1). Find F'(1) if f'(2) = 9.

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Q: x TC 021 Find The Area under the curve Y= 4sine between X=and 2 X= 7, by the double integral method.…

A: This question is based on application of integration.

Q: Certain radioactive material decays in such a way that the mass remaining after t years is given by…

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Q: = A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y -4x²…

A: Maximize area