Prove that f(x) = (x – 1)2 + (x + 1)² is an even function. A function k(x) is an even function if Choose... f(x) is an Choose...

Q: 6.) What is the derivative of f(x) = x| at x= 07 a.) r'(x) = 1 c.) f'(x) = 0 b.) f'(x) is undefined…

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Q: - Evaluate sin 0 if cos 0 = 2/5 and 0 is in quadrant I. Evaluate cos 0 if sin 0 = -1/4 and 0 is in…

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Q: Use the differential to approximate the expression. Then use a calculator to approximate the…

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Q: Find the derivative of the function at the given point in the direction of A. f(x.y,z) = In (x…

A: Solved below.

Q: 1. Coefficients Linear in Two Variables: (x+ y-1)dx+(2x+2y+1)dy=0

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Q: (c) cos 27 (d) tan

A: Cos(π/4)= 1/√2= 0.707106781

Q: 2.s? (s – 1)(s² + 1) 2s – 13 2 s(s – 4s + 13)

A: Let's find.

Q: Give a solution to the system -Lis -10. 2 3 - 15 ¤(0) by solving the IVP with initial condition…

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Q: Find the interval of convergence of the power series (x-2)". n =1n

A: Here we have to find the interval of convergence of the given power series.

Q: (е) cot 57 (f) 5 COS 6.

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Q: 4) lim (ei – 1) x 3

A: Let's find.

Q: Find by implicit differentiation. dx x 6x + 7y = 8 dx

A: we have to find the derivative

Q: 8.) What is the slope of a tangent line tangent to curve g(x) = v5x -8 at point x= 37 a.) 7 b)V7 d.)…

A: Since you have asked multiple questions, we will solve the first question (i.e., Question-8) for…

Q: What is the expanded formula for a family with 8 children? O a + 8ab+ 25 + 56ab + 80a b + 56a b +…

A: Consider a family with 8 children

Q: The answer is incorrect I think because I submitted it on the first time it was.  Kindly resolve it…

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Q: A piecewise function is given. Use the properties of limits to find the indica fix) if x 3 5. if x-3…

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Q: Name the given quadric surface and give its axis. (b.) Sketch the surface. (c.) Name its trace on y…

A: The given equation is: -225x2+100y2+36z2=0⇒-x2602+y2902+z21502=0

Q: 3. In the differential equation (9x - 4y+ 4)dx-(2x – y +1)dy = 0, the lines 9x – 4y +4=0 and -(2x -…

A: here we have to find intersecting point 9x -4y +4 = 0 9x -4y = -4................(1) -(2x-y +1) = 0…

Q: 3. dx

A: Integral CalculusExtension of power formula

Q: Use the differential to approximate the expression. Then use a calculator to approximate the…

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Q: Cost, Revenue, and Profit A company that manufactures sport supplements calculates that its cost C…

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Q: Find the area of the triangle. Round to the nearest tenth. S 16 km 66° R 7.8 km 62.6 km2 11 km2 O 57…

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Q: help

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Q: Find the average value over the given interval. 11) y =x2 - 3x+5; [0, 3] D)- A) 5 B)

A: As we know that; The expression for the average value of the function over the interval a,b is:…

Q: Find maclurine seris sin

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Q: Find the arc length of the curve with parametric equations x = e-t cost and y = e-t sint on the…

A: We have to find the arc length.

Q: lim x⟶0−        f(x)= B) lim x⟶0+         f(x)= C) f(0)= D) Determine whether the function f is…

A: We have to find the limit

Q: 7 х2 + Зx + 3

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Q: Can you transcribe this to an image because I'm having a hard time understanding the equations

A: Here is the image form of the solution.

Q: 3) Find the area of the region bounded by x2 = y and y = 1. a. 1/3 sq.units b. 2/3 sq.units c. 4/3…

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Q: 2. Evaluate ((x +3)° 3x²dx. A) x* +3)* + C B) + 3)* +c D) * + 3}° +C a

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Q: +1)dy/dx+y=lnx If what method of differential equation

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Q: Write the general equation of a line perpendicular to 12x-5y+60=0 and passes through (1,-2).

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Q: (d) tan 꽃 3

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

Q: Find the curvature of the space curve. r(t) = - 3i + (3+2t)j + (t +8)k %3D

A: The given curve    r(t)=-3i+3+2tj+t2+8k

Q: The following series is divergent: n5-2 Σ 5n4 n =1 Select one: O True O False

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Q: An airplane flying at an elevation of 3,500 ft., directly above a straight highway. Two motorists…

A: Let d be the distance between the two airplanes

Q: Solve the triangle. Round your answers to the nearest tenth. a = 23, c= 27, b= 24 mLA = 53.2°, mZB =…

A: The Cosine rule: a2=b2+c2-2bccosAb2=a2+c2-2accosBc2=a2+b2-2abcosC Given: a=23, b=24, c=27

Q: dx 7. S. 9x2+16 tdt 8. S 9. S V25 – 4x²

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Q: 4.For the 2 curves xy = 8 and x2 = 64y, find the angle between the two tangent lines at the !! %3D…

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Q: sV 49 – x2 49 — х" dx

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Q: Calculate the first order partial derivatives and find and df dx dy f(x, y) = /x2 + y² f(x, y) = (x2…

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Q: Express the sum using summation notation. Use a lower limit of summation not necessarily 1 and k for…

A: 2+52+3+72+......9

Q: 8x -2x3+7

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Q: 3z dz (1 – 4z–2z²)²

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Q: Sx? cosh 5xdx

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Q: What is the area of the enclosed regions in problem number 3?

A: We can solve this as follows:

Q: dx Given dt 1 and y = 6. Find for x2 + y² = 100 dt O A. 3 4 O B. 3 4 3

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Q: find f'(x) if f(x) equals the given expression. a. 3x + 2x^2 b. In (cos e-x)

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Q: . Evaluate [10x cos(x²) dx . A) sin(x³)+C C) 30 sin(x') +C 3 B) sin(x') +C 10 D) 3 sin(x') +C 10

A: Our Aim is to evaluate the integral given below:-∫10 x2 cos (x3) dx -(i)