In ² x→∞ 9x Explain why we can use L'Hopital's Rule in this problem. Use it to find the limit. Consider lim

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A: The given function is

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Q: 1. [xds, where C is the curve y=x², z = 0 from (0, 0, 0) tom (1, 1,0)

A: 1.∫Cxds,where C is the curve y=x2,z=0 from (0,0,0) to (1,1,0)y=x2 from (0,0) to (1,1)Let…

Q: Evaluate the spherical coordinate integral 2π π/3 3 S S S 4p² sin dp do de. & 0 seco

A: I=∫02π∫0π/3∫sec⁡ϕ34ρ2sin⁡ϕdρdϕdθUsing the Power Rule∫xndx=xn+1n+1+C

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Q: 40 b) lim- 0-0 tan(20)

A: To find:-

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A: The objective of this question is to find the intervals where the function f(x) = (x+4)^2/3 is…

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A: The equation of line passes through points  is

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Q: 1 Let R be the region in the first quadrant below the curve y Compute the volume of the solid…

A: Region is bounded by y=11+x2 from x=0 to x=1.Rotating the region about y−axis.Using the shell method

Q: Find a power series representation of for f(x) = convergent, find its sum. x+2

A: f(x)=x2x+2We know the power series of 11+x11+x=∑n=0∞(−1)nxn

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Q: Find the binomial series for the function (1 – 6x)³. (1-6x)³ =

A: Function:

Q: and find If f and g are continuous functions with [3f(x)dx = 36 [*5g(x)dx = -21, [*{3g(x) – 4ƒ (x) —…

A: f and g are continuous function

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A: Conversion form degree to radians

Q: ,11 h(x) = x¹¹ arcsec(x).

A: h(x)=x11arcsec⁡(x)h′(x)=ddx[x11sec−1⁡(x)]Product Ruleddx[f(x)g(x)]=f(x)g′(x)+g(x)f′(x)

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Q: Question 10 If f is odd and f is differentiable, then f' is odd. O True False

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Q: Consider the following relation. y = x + 2 Step 1 of 2: Find four points contained in the inverse.…

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Q: Find af ?х af ду af дz af af 7 Әх ду ах af = = ду af = af дz f(x, y, z) = 3xy + 3xz - 3yz Find their…

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Q: The 4th degree Taylor polynomial for sin(x) centered at a = is given by the following. sin(x) = 1 +…

A: Rewrite asx=39

Q: In preparation for the NEXT problem, calculate the derivative of the SINGLE VARIABLE function. f'(x)…

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Q: ve the equation. 2 sin ²0-sin 0-

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Q: c) h(x)=√e. '+e

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Q: 22. A light shines from the top of a pole 15 m high. A ball is dropped from the same height from a…

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Q: Given that 3 L³ex ex dx = e³ - e, use this result to evaluate [²³3 3ex + 2 dx.

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Q: The demand equation for a certain product is 6p² + q² = 1,200, where p is the price per unit in…

A: The demand equation for a certain product is 6p2+q2=1200,where p is the price per unit in dollars…

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Q: b. C. 8 x3 x5+2 d. So 8 dx √₂ √x²-x dx dx x+√x

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Q: - Eliminate the parameter to find the Cartesian equation for the curve represented by the parametric…

A: Given that the parametric curve

Q: 4. Prove that if f is continuous on [a, b], then en | S" 1(x) dx | ≤ f f(x)|dr. f(x)dx a

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Q: Calculate af ax af Əy = af af af af ax' ay ax (1,-1) ду f(x, y) = e0.9xy = ax (1,-1) af ay (1,-1)…

A: f(x,y)=e0.9xy

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A: Given that the function F(x) is defined as The figure

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A: 1 \text{or r is infinite, the series is divergent. }\\ &amp;\text{If }r=1, \text{the test is…

Q: 2. Consider the curve y = sinx - on the inteval 0 ≤ x ≤ π/2. (a) Sketch the curve and shade in the…

A: (2)The curve is given as, on