Find dy dx In (y²) = 4x + 5 - dy dx dy dx dy dx dy dx = = - = 2y -2y 2 K|N Y 2 У

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) =x² + y² subject to the…

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Q: y = xer

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Q: 1) fx²e-³x dx

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: (a) Find the unit tangent vector on the curve r(t) = [cos(t), -t, -4sin(3t)] when t = 0. (b)…

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Q: Give the partial fraction decomposition for the following function. 2 x²-2x-8 2 2 x-2x-8 ||

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Q: Let f(x) = -x+7 and g(x) = x^2 -2 evaluate the expression f(g(1))

A: We have to find f(g(1)) for the given function. It is a example of composite function. We replace x…

Q: Describe the x-values at which the function is differentiable. x² y = x² - 49

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Q: (a) Find the unit tangent vector on the curve r(t) = [cos(t),2t, 3sin(4t)] when t = 0. (b) Evaluate…

A: Given curve:Unit tangent vector is given by,Therefore,

Q: The graph of y = f(x) is given below. -5 150 num -4 lim f(x) AI-1 -3 -2 5 4 3 2 -1 -1/ 1 2 4…

A: A graph of the function  is given.The aim is to find the given limits.

Q: Use spherical coordinates. Evaluate xex + y2 t2 + dV, where E is the portion of the unit ball x² +…

A: To find  E is the portion of the unit ball  that lies in the first octant

Q: 7. u = (2, 2), v = (2, −2) 8. u = (2,-2), v = (−2, 2)

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: Find the area of the shaded region. -1.0 -0.5 y 8 6 y=3e 4 2 0.5 (1, 3e) y=3xet² 1.0 1.5 2.0 X +

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Q: Calculate the L4 approximation for f(x) = cos² x on TU I 4 2

A: The left Riemann sum∫abf(x)dx≈Δx(f(x0)+f(x1)+f(x2)+⋯+f(xn−2)+f(xn−1))Δx=b−an

Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x+y=5,…

A: Equation of plane : and equation of cylinder : Find the volume of the region in the first octant…

Q: Let f(x) = 2x³ + x²-x+3 on the interval [-1.5, 5]. Use calculus and algebra to justify all answers.…

A: The given polynomial function is  on the interval .

Q: Find the domain of the function. f(x)= x-1 X+2

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Q: 2. Find the derivative: a. y=ln(e^x)/(1+e^x)

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

Q: b.Let f(x)=x²-3x² -1, x ≥ 2. Find the value of af dx at x = -1.

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Q: An account earns an APR of 4.7% compounded as often as imaginable ("compounded continuously"). The…

A: The given rate is, r=4.7%=0.047 compounded continuously.For the continuous compound, the annual…

Q: Differentiate the given function. 8 (71 + 1/ ) (71²-9) F(t)= 7t =

A: we need to differentiate the given function.

Q: Find the general solution of the first-order linear equation dy dx + 2y = e²x

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Q: Determine if the series diverges. If it does diverge, type a upper case D as your answer, and if the…

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Q: Use partial fraction decomposition to find the following integral -da 24-1

A: I=∫x2x4−1dx

Q: 4 Sª 3 16 (x-7)(x + 9) dx

A: I=∫3416(x−7)(x+9)dx

Q: Find the lines that are tangent to the curve y=2tan(pi*x/2) at x=1

A: The equation of tangent line passes through point  with slope

Q: 3. Given that w = xyz + y² + x + 1, x = et, y = 82, 2=t+1. ) Find Ow/as. (b) (c) Find 0w/Ot. Find…

A: Given that .(a) To find .(b) To find .(c) To find .Note: Since the student has posted many sub-parts…

Q: Find the general solution: y" + 5y' + 5y = 0

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Q: The temperature at a point  (x, y)  is  T(x, y),  measured in degrees Celsius. A bug crawls so…

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. tan(5x…

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Q: Let A(x) = f(t)dt, with f(x) shown in the graph below. 4 3 2 1 X -1 -2 -3 -4 -5 A 5 At what x values…

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Q: The temperature at a point (x, y) is 7(x, y), measured in degrees Celsius. A bug crawls so that its…

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Q: Solve the given boundary-value problem. y-10y+25y=0, y(0)=1 y(1)=0

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Q: Given the following integral and value of n, approximate the following integral using the methods…

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Q: Describe the x-values at which f is differentiable. (Enter your answer using interval notation.) X…

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Q: differentiate. do not simplify f(y) = (3-y^3)^3/4

A: given function

Q: a 5. At 2:00 PM jogging at 8.5 mph. starts from the same place, heading East at 60 mph. the driver…

A: At 2:00 PM a runner heads east on a highway, jogging at 8.5 mph. At 3:00 PM, a driver starts from…

Q: 9. Locate all relative maxima, relative minima, and saddle points of the fol- lowing function f(x,…

A: The given function is

Q: Q/ solve equations 1- y' = ky 2-x(1+y²) dx =y(1+x²) d;

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Q: (a) Find the unit tangent vector on the curve r(t) = [cos (t),2t,3sin(4t)] when t = 0.

A: To find the unit tangent vector on the curve .Note: Since the student has posted multiple questions…

Q: = O Trigonometric Identities and Equations Proving an identity using fundamental trigonometric…

A: 1+tan2x

Q: Find the volume of the region between the cylinder z = 2y² and the xy-plane that is bounded by the…

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Q: Find the points on the curve where the tangent is horizontal or vertical. You may want to use a…

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Q: +² dt F(x) In(t) F(x), determine whether F is inc a dec x>2 at x=2020

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Q: Suppose $23,000 is invested in an account with an APR of 4.9%. If the interest is compounded…

A: Here we have, P=23000r=4.9%=0.049t=10 years.The compound interest is given by,

Q: ·b f(b) − ƒ(a) = f'(a)(b − a) – ſå ƒ''(x)(x − b)dx a

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Consider the following differential equation to be solved by the method of undetermined…

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Q: Isolate 9.\ 2 5 = 22 gt² + vt gt² + avt ??? 25 = 25= 2 ut(+ +2 g = expected: -avt + $25 t²

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