Which statement is true for a function f(x)? b The average value of a function is [ f(x) dx. a f '(b)-f'(a) b-a O The average value of a function is b So f(x) dx a The average value of a function is b-a O The average value of a function is not given by an integral.

Q: Use the linear approximation to estimate In (√0.99).

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Q: Evaluate the following limit, if possible. If the limit c 4 lim 42-√√

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Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

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A: Let's find volume of solid (V) = ?

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A: Given that,

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Q: Let f(x, y) = − sin2 (2x − y) Evaluate fx and fy at (π / 4, π / 3)

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Q: x-1 x² + 5x + 8 S dx

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Q: Evaluate the improper integral or state that it diverges. P -dx Select the correct choice below and…

A: The given integral is: I=∫2∞32x2dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

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Q: Problem Revolve about the (a) x-axis and (b) y-axis the area enclosed by y² = x and y=x³.

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Q: Integrate the following (3x + 5)dx 1. S (x - 1)(x² - 1) -

A: Given:∫(3x+5)dx(x-1)(x2-1)Perform Partial…

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A: Given problem:-

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Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…

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Q: Evaluate f(x³ -x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

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

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Q: Find the absolute extremum values of f(x) = xe² xez-2x² 3 on the interval [0, 1]. (Note: ez ≈ 0.22)

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Q: 4. (x³ − 2x² + 1)dx [³ (x² - 2x + 5)²

A: The integral to be evaluated is ∫x3-2x2+1dxx2-2x+52. The first step will be to do a partial fraction…

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A: Given query is to find the equation of the tangent.

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Q: Given that sin(0)= TT 3 and 2 <0<π what is the exact value of cos(20)?

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Q: What is the volume in cubic units of the solid formed when the region. bounded by y = x^2 + 1, y-…

A: Given :y=x2 + 1, y-axis , x-axis and x=2 is revoloved about x=-2.Formula :Volume in…

Q: (6) Sketch a graph of a function, f, that has the following properties: • lim f(x) = 3 and lim f(x)…

A: Given information:  ----------------------------------------------------------------------------…

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Q: A study indicates that the population of a certain town will be growing at the rate of p' (t) = 5 +…

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Q: What is the the x-axis and the semicircle y = (4 - x^2)^1/2? O 0 02 Ο ΝΑ x-coordinate of the…

A: Solution is given below:

Q: C. Find the slope and the equation of the tangent line to the curve. 23. y 2x−x+2 at (-1,5) 24.…

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A: A detailed solution is given below.

Q: lim x++∞ x² + x e²x + Inx

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Q: etermine the instantaneous rate of change of the function πt √√x sin (772³) dt : x = 1. x3 1 + √t

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Q: Can you solve this and show work clearly, the first part is X to the 3

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Q: Convert the rectangular equation x2 = −2y2 + 5x2 y2 to polar equation

A: The rectangular equation is x2=-2y2+5x2y2

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Q: The curve has an equation of r = 4sin0. Compute the area bounded b the curve. 12.57 11.18 16.89 O

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A: A detailed solution is given below.

Q: 10x-3y For the function f(x,y,z)= 8z + 1 fx=0 find fx. fy. fz, and fyz-

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: The equation of the curves are: C1: y = x2 ⇒ x = y                 for first quadrantC2: x = y2 To…