6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

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A: Given that      Region R : 0≤x≤1 , 0≤y≤1-x2 , 0≤z≤4-x2+y2    Now, we take…

Q: Perform the following integration. 1. (sinhæ)(coth? a+csch® a) dự sec³ x tan x 2. S dx √2 + sec x 3.…

A:

Q: II. Evaluate the following integrals. fe (sin³x)√1 + cos x dx 2.

A: ∫π/2πsin3x1+cosxdx sin3x=sinx(sin2x)=sinx(1-cos2x) ∫π/2π(1-cos2x)(1+cosx)sinxdx let 1+cosx=t…

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A:

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A: Given ∫-∞∞dxx2+1To evaluate the integral:

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Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

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A: This question can be solved using the concept of limits.

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A: derivative

Q: Answer

A:

Q: What is the general solution to the differential equation (tan x)dy - (4y In y - y tan³x)sec²x dx =…

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Q: I. Evaluate the following limits. 1. lim sinh r → r r→0 sinhr – r

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Q: 2 cos xsinx V2+cosx 1. S- -dx

A: Given

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A:

Q: approaching

A: Please refer to the image below

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A: topic- inflection points and concavity

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A: Use area under curve

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A:

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Q: PLEASE SHOW COMPLETE SOLUTION.   Find each of the two areas bounded by the curves y = x^3 − 4x and…

A: Follow the procedure given below.

Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A: This question is related to rate of change, we will solve it using given information.

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A: First we draw the graph,

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A:

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A:

Q: Jill burns 100 calories per hour while sleeping, 300 calories per hour while walking, and 200…

A:

Q: 4. An object is moving along a horizontal line according to the position function s(t) = 2t³ - 21t²…

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Q: it possible to get the area = 3x and y = x³, usi a. vertical strips b. horizontal strips

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A: 1+y2 dx+x2y+y+2xy dy=0

Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A: Given problem:- Suppose y = f(x) is a curve that always lies above the x-axis and never has a…

Q: Evaluate the following limits. 1 - cosh x 1. lim x+0+ ln(x² + 1)

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: In x 2. Use a local linear approximation of f(x) = 1+x² to estimate In (0.9) 1.81

A:

Q: ways

A: Please refer to the image below

Q: Is that pi (π)? Or something?

A: Given ,  Area of the region bounded by  y = cosx , x = -π/2 and x = π/2 and the x - axis  We have to…

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Q: II. Evaluate the following integrals. 1 - coth² (log₂x) dx rcosh (log₂x) 1. S

A:

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Q: VI. Determine the instantaneous rate of change of the function √x sin (³) In 2 = = [X² f(x): dt 1 +…

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Q: Determine the derivative of the following function. Do not simplify.  y = (x - 2)3√2x-1 (sqaure…

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A: Given problem:- A group of management students are creating a business plan for their proposed shoe…

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A:

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A: To evaluate the following definite integrals using the Fundamental Theorem of Calculus.c ∫164t-1t+t3…

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Q: solving the following differential equations (x + tany)dy=sin ey dx

A: On solving this we will get

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A: The following differential equation is a Bernoulli equation:dydt+yt=y23 where y=ftBy making the…

Q: Find the area of the region bounded by the curves y = 1 (x+1)21 2 y = 4 and

A: Please refer to the image below