noiteims 64. At what point on the curve y = 1 + 2e* - 3x is the tangen line parallel to the line 3x - y = 5? Illustrate by graphing the curve and both lines. start ord örlt dieem

Q: 4b. If w= In(4xy) dw cos(2yz - 3), x = log(t), y = 4et² and z = sin(t³ - 1). Find dt

A: Let's find partial differential of given function.

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A: Given :st=e2tsin7t

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Q: 7. Given tan 0 = 2, sketch the angle in standard position and find cos 0 and sin 0, where 0…

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Q: 3. If f, g and h are functions so that the composition makes sense, then the composition of the…

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Q: If the average rate of change of biomass (in mg) of a bacteria culture from time t = 2 hours to t =…

A: To find the biomass at t=14 hours

Q: Obtain the general solution. (HOMOGENOUS EQUATION) 1. 2(2x² + y²)dx - xydy

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Q: Question 6 y" - 4y + 4y = 4 cos 2x y(0) = 2; y'(0) = 5 Use the editor to format your answer

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Q: Find the surface integral of the field F(x,y,z)=8y i - 8x j + k across the portion of the sphere x²…

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Q: Express y = = In(2t), y = 1- t in the form y = f(x) by eliminating the parameter.

A: Given: x = ln(2t) and y=1-t Solving for x in terms of t. x=ln((2t) Take exponential on both sides,…

Q: 3. Find the area of the shaded region. f(x)=√x+1 f(x) 1 -x-1

A: To find the area of shaded region

Q: 5. Given the region R on the right, use vertical strip, SET UP the double integral that will solve…

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Q: In this question, we will approximate 83 with a rational number. a)To use the linear approximation…

A: To solve the following problem

Q: Use power series to integrate f(x) = X 1+xA

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Q: d. fr³ (2 – r²)¹² dr 12 e. f (nt)² dt t ex f. So 2₁-2x dx

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Q: (x), 1x²+1 (X-2)2 ++요 3

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the work required to pump water out of an inverted cone that is 10 meters tall with a radius of…

A: We have to find the work required to pump water out.

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A: To find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

Q: f 12 sin(x) cos(x) dx

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Q: I. In a triangle, the base is increasing at a constant rate of 2.8 centimeters per second, while the…

A: Figure:-

Q: gle has two of its adjacent sides measured to be 2 and 3. The included angle between the said two…

A: Let's estimate new area of triangle.

Q: Evaluate the integral. S(7x + √x) dx Š(7x 1 (Type an exact answer.) 'x + √x) dx = [

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Q: ƒ(x) = 3x³ – 2x, [−1, 8]

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Q: Use Newton's method to approximate a root of the equation 3x^(7) + 2x^(4) + 2 = 0 as follows. Let…

A: The given function is: 3x7+2x4+2=0Initial approximation is:  x1=2

Q: 5. At a certain point on the beach, a post sticks out of the sa the beach. The depth of the water at…

A: “Since you have posted multiple questions we will solve first three subparts for you. To get…

Q: Find a power series representation for fx arctan(x)dx. You can use the sigma notation or the 1…

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Q: Suppose that f is defined everywhere and x = -2 and x = 1 are the only critical numbers for f. If f"…

A: To determine whether the given statement is true or not

Q: FOLLOW

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Q: Evaluate the double integral on the given region. [ (5x2 (5x² + 8y³) dA; R:5 ≤ x ≤ 7 and 3 ≤ y ≤4 R

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Q: (2) f(x) = 1 + √I. (a) Find f'(1). (b) Find an equation of the line tangent to the graph of f at x =…

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Q: Complete the following steps for the given function, interval, and value of n a. Sketch the graph of…

A: We have to find the midpoint Reimann sum.

Q: QUESTION 12 Differentiate with respect to x: f(x)=xsinx O f'(x) = sinx+xcosx Of'(x)=xsinx+cosx O…

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Q: Use an appropriate test, and clearly indicate which test you are using, in order to determine…

A: For (a), The nth term is 1n8+5n. And notice that 1n8+5n≈1n8. Now,                  limn→∞…

Q: Use only the fact that 6x(4-x)dx=32 and the properties of integrals to evaluate the integrals in…

A: we will  find the required.

Q: Question 2 2. y' +10y=x²y(0) = 0 Use the editor to format your answer

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Q: Show that, for any function w(u, v), w(x, y, z) defined by I+Z w(x, y, z) = w(u, v), u = . satisfies…

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Q: Consider the integral A. Sketch the region of integration. B. Convert it to polar coordinates. C.…

A: We need to integrate :

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Q: Find the matrix A' for T relative to the basis B'. A' = T: R² → R², T(x, y) = (−8x + y, 8x − y), B'…

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Q: (3x + 2)²D² +3 (3x + 2)D − 36, = 3x + 4x + 1

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Q: Find the area bounded by y=xsinx and the x-axis from x=0 to x=πT.

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Q: 5. Use a trigonometric substitution to evaluate the indefinite integral [ I² - x²) ² dr

A: To evaluate the integral.

Q: Use the root test to determine if the following series converges, diverges or is inconclusive…

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Q: • xª ex+ln2x³ x² b. S dx

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

Q: Using integration by parts only fx sin(x) dx Provide your answer below:

A: Topic:- application of integration