A. Evaluate each of the following definite integrals. 2 S (8x3 + 3x2) dx 1.

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Q: 7. There is a removable discontinuity at x = 1 and f(1) = 4 %3D

A: 7.  There is a removable discontinuity at x=1 and f(1)=4

Q: Suppose that the total profit in hundreds of dollars from selling x items is given by P(x)=5x-5x+7. ...

A: Average rate of change of f(x) as x changes from a to b is given by, A(x) = [f(b) - f(a)]/(b - a)

Q: 33. lim arctan(e*)

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Q: Given r(t) 12ti + 5cos ti + 5 sintk, find the unit binormal vector and torsi =

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Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the oute...

A: Given :y=x9+5To find : (f(u),g(x)) , dydx and G'(u).  

Q: 2. Let f be the function f(x)= arctan.x. (a) Find the third Maclaurin polynomial for f. (b) Approxim...

A: To find the maclaurin polynomial for f.

Q: Find the derivative. 1. y = Vx2 – 5 2. y = (2x? – 1)3(3x² + 1)3 (3x²-7)* (3x²+5)4 %3D

A: Since you have posted multiple questions I can do first three question as per our company guidelines...

Q: Prof Applications of Derivatives the given condition. 1. r 2 cos 30 at 0 = 4. Solution:

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Q: 1 94. Prove that the derivative of f(x) = In x is f'(x) %3D by completing these steps.

A: The given function is f(x)=ln x

Q: Determine S5x? cos 2xdx

A: Given query is to evaluate the integral.

Q: Decimal fractions: Comparing and ordering Lhance High Jump Competition Height (m) Three athletes com...

A: Given:  Willia : 1.85   Trina : 2.02   Sumi : 1.7

Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What val...

A: solution:-f(x)=4x3+17x2+13x+36x+4     x<-45x2+2x+a                       x≥-4f(x) is continuous a...

Q: 5. lim f(x) = +0, lim f(x) = 0 lim f(x) = +o, lim f(x) = 0 x-1- x-1+ x-1- x-1+ and f(-1) = 0 and f(-...

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Q: A retarding force, symbolized by the dashpot in the figure to the right, slows the motion of the wei...

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Q: (6x3 +7x2 + 20x + 16 d.x Consider the indefinite integral x4 +4x2 Then the integrand has partial fra...

A: We need to solve integral.

Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

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Q: 6. A survey of 200 students is taken to determine their super powers. 120 of them had super strength...

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Q: A. Evaluate the following integrals.

A: Given that: ∫x(x2-2)14dx

Q: (х+2)* x² – 4 dy 2y dx x? - 4 х —

A: Given  :        dydx+2yx2-4 = x+22x2-4

Q: ) H (æ) = 13- 2a+36a -2 then f is concave down ou (A) (-0,-3) and (-3, 0) %3D (B) (-, -3) and (2, 00...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: coS X =dx sin? x

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Q: A manufacturer is making a special voltage small electronic battery. The total cost, C, (in thousand...

A: We need to find maximum production level.

Q: Check the differentiability and continuity of the function below.: 3x 1. f(x) = 2. f(x) = 5- x² at x...

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Q: 6. Let f(x, y) = x3 – xy+ y. Find the critical points off and determine if they are local minima, lo...

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

Q: Find the value of the constant k that makes the function continuous. 2x-2x-12 if x+3 g(x) = , x-3 kx...

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Q: Given the graphs of f(x) and g(x), determine the value of expressions below. y f(x) y = g(x) lim (f(...

A: From the given graph, we can find the following limits: limx→2f(x)=0  limx→2g(x)=0 limx→1g(x)=1 limx...

Q: dH f(5) = 8, f' (5) = 4 f(26) = 8, f'(26) = 6, g(5) = 1, g'(5) = -9, and H(x) = f(r² + g(x)). Find d...

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Q: 2. Find equations of the tangent line and the normal line to the curve y = 1+ x2 at the point (1, 3)...

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Q: S S( 3x² +x³y)dxdy

A: Evaluate ∫13∫023x2+x3ydxdy=?

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Q: Monthly sales, S, of a product (in $1000) is a function of the monthly advertising (in $1000), a, sp...

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Q: cos t dt 1 + sin t 37.

A: The given integral,37. ∫cos t1+sin tdt

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Q: coS X =dx sin? x

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Q: 725 + 7z4-2r If f(z) , find f'(z) Add Work

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Q: Evaluate the limit. lim-3 Væ²+7-4 3-x 0 -등 5 6 - 8. 6 8 O None of these

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Q: #9 all

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Q: Evaluate the integral: -dz (A) Which trig substitution is correct for this integral? Oz= 17 sin(0) z...

A: Given that: ∫17x2-9x4dx

Q: Determine whether the equation is exact. If it is, then solve it. (3x'y +2 ) dx+ (x-3) dy D0

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Q: Express the repeating decimal as a fraction. 0.904818181818... 0.904818181818.=

A: Let X equal the decimal number. X=0.904818181818...             (1) With 2 digits in the repeating d...

Q: 17. Let f be the function defined by f(x) = . What is the average value of f on the interval [4, 6] ...

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Q: 10. Let f(x, y) = x²y + y. Find the minimum and maximum values of f subject to the constraint x² + y...

A: Given: fx,y=x2y+y The constraint equation is: gx,y=x2+y2=5   Now apply the Lagrange's multiplier; ∂f...

Q: Find the derivative of the function. y = 9Vx y' = %3D

A: Our Aim is to find the derivative of y=9x -(i)

Q: Write your complete solution on the box provided after each number. Determine the standard form of t...

A: Solution of General equation of ellipse is written in step2 and 3