1: Find the area of the region bounded by the graphs of x = y², y = x + 3, y = -3 and y = 2.

Q: (6w+12w") /w +w° dw

A: Given: I=∫6w-4+12w-7w-3+w-64dw So, we can also write as: I=∫6w-4+12w-7w-3+w-64dw=∫6w4+12w71w3+1w64dw...

Q: 2- Prove that: Jzt=27 dz %3D 2in. Whot is the princinle nart for f(z) = ze %3D

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

Q: Find the area of the triangle with vertices P(1, 4, –2), Q(0,0,0) and R(4,5, 1). NOTE: Enter the exa...

A: We can find the area as below.

Q: Find the directional derivative of the function at the given point in the direction of the vector v....

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Q: A Given yesin (ITX2)= InGe) XyZ of Find Zx and Zy.

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Q: Evaluate the following integral. | e2* cos3x dx

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Q: 2x2 (7) Let f(x) = Find the vertical x2 –1 and horizontal asymptotes of the given function. Show the...

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Q: Find the coordinates of the centroid of the solid generated when region bounded by x2 + y? – 4y = 0 ...

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: I am attaching image so that you understand each and every step.

Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

Q: B - Find the equation of the curve whose slope at any point p(x.y) is m = x(x+5)?, and passing throu...

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Q: Suppose f is a function such that f'(7) is undefined. Which following statements is always true? a. ...

A: for the define f'(7) the function must be contineous at 7 but here undefine is given so  answer is b...

Q: B. dx (9-22)²

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: Find the tangent line approximation T to the graph of f at the given point. Then complete the table....

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Q: 4. Sdz 「号

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Q: Find the exact value of the trigonometric expression given that sin(u) = - where 3x/2 <u< 2x, and co...

A: tan(u+v) = (tanu +tanv)/(1- tanu*tanv) tanu = sinu/cosu cosu = 1-sin2u cosu = 1-(3/5)2 cosu = 4/5 si...

Q: Consider the following. f(x, y) 3e% sin(y) Find Vf(x, y). Vf(x, y) = %3D Determine Vf(x, y) at the p...

A: f(x,y)=3ex siny∇f= ∂f∂x i + ∂f∂y j∇f=3sinyddx(ex) i +3exddy(sin y) j∇f(x,y)=(3ex siny, 3excosy)at 0,...

Q: Q3 : Evaluate the following integral. x+V9-x2 xps

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Q: 2. f (x) 3 - 2x² if xくQ こ 2 メ if x 2 2

A: f(x)= x3-2x2 ; x&lt;22-x ; x≥2       a=2 , if f is differentiable , then f'(2) should be finiteusing...

Q: DO NOT include spaces in between characters. * 7 Given y=(3x +6)| 2x– Find the value y' at x = 4

A: Given:       y=3x2+62x-14 Differentiating on both sides with respect to x.      y'=ddx3x2+62x-14 App...

Q: Find the volume of the following solid. The solid above the region R= {(x,y): 0<x<2, 0sy<4-x} and be...

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Q: 6. Find the minimum surface area of a box that holds 2 cubic meters.

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Q: Activity 4: 1. Find the indicated derivative for each of the following functions and evaluate as ind...

A: We know, ddxxn=nx(n-1) , for any real number n. ddxcos x= -sin x ddxsin x= cos x

Q: Consider the following. f(x) = 3x – 6 cos(x), -2 sxs0 Use technology to estimate the absolute maximu...

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Q: For items 5-7: Given that f(x)dx = 3 and g(x)dx = 4, evaluate 5. [4 f(x)– 3 g(x)]dx А. 12 В. О С. 24...

A: Let's find. 

Q: e2x dx Evaluate: 9-4e4

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Q: dx x4 V9 – x2

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Q: Find the area of the triangle with vertices P(1,4, –5), Q(0,0, 0) and R(2, 4, 1). NOTE: Enter the ex...

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Q: Find d'y /dx? Y = xtan (=)

A: d²y/dx² means we have to calculate second derivative of the function.

Q: 2+ x, x lim g(x) c. g(2) < lim g(x) d. g(2) # lim g(x) X-2 X-2 X-2 X-2

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Q: Find the indefinite integral using the substitution x = 4 sin(0). (Use C for the constant of integra...

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b). (Select all tha...

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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

Q: S(*-4)(12: – z') dz

A:

Q: 3. у?dx + (x2+ 3ху + 4у?)dy %3D 0; when x —D 2, у %3D 1

A: Explanation of the answer is as follows

Q: 1 Find an equation of the line tangent to y at point (0, -). X-3

A: Given y=1x-3 at point 0,-13 To find equation of line tangent:

Q: Question 7 of 8 > -/5 View Policies Current Attempt in Progress Consider the points A(1, –1, 4), B(2...

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

A: Vectors with opposite directions have 180° angle between them.x and y components have opposite signs...

Q: 3. The statement f(x) dx = [ f(y) dy is, A. true B. false C. sometimes true D. neither true nor fals...

A: Given,            The statement is ∫abfxdx=∫abfydy.To find : Check whether the statement is true of ...

Q: b) Show that y = 2sin (2x) is a solution to the differential equation: - 64 =0

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

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Q: a. Use integrals to show that the circumference of the circle z2 + y? = a² is 27a. %3D b. Find the l...

A: Given that equation of circle x2+y2=a2center of circle 0,0  and radius =aSolution :x2+y2=a2y=±a2-x2o...

Q: A group of 13 workers decides to send a delegation of 3 to their supervisor to discuss their grievan...

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. (x³ + 1)² dx

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Q: Find F'(x) if F(x) = cot¬13

A: A detailed solution is given below

Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 6j + 9k and the vector component of v ort...

A: We know that, vector component of v on b is v.bb2.b Therefore , vector component of v on b is =(2i^-...

Q: Prove that lim (4x² – 25) = -9. X→2

A: We will prove this by definition of limit as follows 

Q: The rose r = asin 30

A: Solution is given below: