Find f'(x) and simplify. f(x)= Which of the following shows the correct application of the quotient rule? O A. OB. O C. O D. X x + 34 f'(x) = (x)(1)-(x +34)(1) [x+34]² (x+34)(1)-(x)(1) [x]² (x)(1)-(x+34)(1) [x]² (x+34)(1)-(x)(1) [x+34]² ...

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A: By using the following substitution we can convert the Cartesian equation to polar form. x²+y²=r²…

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A: Select one

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A: This question can be solved using the concept of exponential growth model.

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A: We have the graph of f'(x) and  we need to tell where f''(x) is >0So, f''(x)>0 when f'(x) is…

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A: Maxima minima, directional derivative

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Q: What is the value of the integral Select one: O 64 O 16 O None of these O 32 08 0 X 2xydydx?

A: Given: I=∫04∫x42xydydx   As we know the Power rule: ∫xndx=xn+1n+1+C

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Q: S 2 1-a Select one: O True O False e²e³dydx = - (₁ e²d²) (²* eºdy) (² dx 2

A: Given :∫01∫21-xexeydydx=∫01exdx∫21-xeydy

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Q: ⁹1 9x + 7 8x5 dx || +C

A: Given: ∫9x+78x5dx

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A: It is given that, C(x)=7+2x+48     ,    0≤x≤50 We have to find the value of C'(8).

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Q: a) Determine if the geometric series 8-1 gn+1 Σ n=1 is convergent or not, and find its sum if it is…

A: Given: ∑n=1∞8n-19n+1

Q: What is the value of the integral Select one: O 64 O 16 O None of these O 32 08 CO 2rydydz?

A: Given:       ∫04∫x42xy dy dx      =∫04∫x42xy dy dx     Taking out constant        =∫042x∫x4ydydx…

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Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

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A: To find the gradient vector of the functionf(x, y, z) = ln(yx)-x2

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A: ∫02∫12x-3y2dydx=∫02x-7dx=-12

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Q: 8. Graph the curve and find the area that it enclosed: r = 2 cos(0).

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Q: (9x - 8) dx || +C

A: Solution of given question is written in below steps.

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A: I have calculated the limits

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Q: Given: f(x) = x³ – 6x² − 15x + 7. Find the LOCAL MINIMUM point of f (x). A. (5, ƒ (5)) B. (−1, ƒ…

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A: Suppose that f(x) (here f(n)=an) is a continuous ,  positive and decreasing function on the interval…

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Q: 10. Find a Maclaurin series which represents cos(x) for every real number around the point a = 0.

A: As we know the Maclaurin series;  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+fiva4!x-a4..... Where…

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A: Given z=f(x,y) D(3,-1)=4 and fxx(3,-1)=-5

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A: Given that fx,y=xey+2y at the point 2,0 and θ=π3 find the directional derivative

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Q: Find the relative extrema of the function, if they exist. 3) f(x)= 3x4 + 16x3 + 24x2 + 32 4) f(x) =…

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Q: A coat of paint of thickness 0.5 mm is applied evenly to the surface of a sphere a radius 20 cm.…

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Q: Consider the function f(x, y) = y ln x - x ln y - . a Find the directional derivative of f at the…

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Q: 9. Find if x (t) = t + sin(t), and y(t) = t - cos(t). doe

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Q: Let R be the region bounded by y = 2x, y = 2 and x = 0. Sketch the region R and evaluate the double…

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Q: n 1 ² Σ (sec (2 + ²) - 2 (2 + ² +)) - nxn i=1 3. Express lim as a definite integral, f(a)da.

A: This is a integration problem

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