Extrema on a sphere Find the points on the sphere x² + y² + z² = 25 where f(x, y, z) = x + 2y + 3z has its maximum and minimum values.

Q: Answer the following questions for the function f(x)=x√x² + 36 defined on the interval -4 ≤ x ≤7.…

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Q: Show that the function y= x ln x is a solution of the differential equation xy" - y' + (1/x) y = 0.

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Assume that  are both  differentiable  functions of t.(a) To find , given that (b)  To find , given…

Q: =D x. 19

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Q: Consider the curve r(t) = tcos(log(t))i + tsin(log(t))j. Is the velocity constant? Is the speed…

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Q: If y xy + x² + 1, then when x = 01/1/12 0 - 12/1/20 O nonexistent O -1 O-2 -1 dy d = ? dx

A: we need to find out the derivative of the function at the given value of x.

Q: HOMOGENEOUS DIFFERENTIAL EQUATION Solve the following differential equations using HOMOGENEOUS DE.…

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Q: 94. Can you have a finite absolute maximum for y = ax²+bx+c over (-∞, ∞o)? Explain why or why not…

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Q: Consider the integral approximation T20 of fo 2e-4 dx. Does T20 overestimate or underestimate the…

A: Here And Now,         ..........(1)

Q: Write the equation 52 = 25 in logarithmic form.

A: Write the equation  in logarithmic form.

Q: Solve the following initial-value problem: dy dx = e sin x 2xy e cos x + x² y(0)=0

A: Given differential equation

Q: Find the interval containing x = 0 where f(x) = 81x - tan(x) is increasing. Write your answer as an…

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Q: (Order your answers so the x-coordinates are in order from least to greatest.) f has ---Select---…

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Q: Find the area bounded by the given curve. r = 6 cos(30)

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Q: Find the first partial derivatives of the function. f(x, y) = 7xy fx fy -

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Q: 600-lb cable is 100 ft long and hangs vertically from the top of a tall building. (a) How much work…

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Q: Given that (fog)(x)=x-8, which are correct rules for f(x) and g(x) that result in this composite…

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Q: Homework Question 3.41) A) Consider the differential equation y*+4²y=0. Verify by direct…

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Q: Find the equation of the tangent plane to the surface determined by x³y² + z-30 = 0 at x = 3, y = 5.…

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Q: Find the largest product the positive numbers x, y, and z can have if x+y+z² = 16.

A: x+y+z2=16Find the largest product of the positive numbers x, y and z.

Q: (a) Estimate the area under the graph of f(x) = 1 + 2x² from x = -1 to x = 2 using three rectangles…

A: We have given that, the function is    , x = -1 to 2.(a) For n=3, we have the right Riemann sum…

Q: Use the quotient rule to find the derivative of -10 sin(x) - 1 6x² +5 You do not need to simplify…

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Q: 18. Find dy/dx by implicit differentiation.

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Q: he graph of the derivative g' has exactly two roots. Complete parts a through c. OB. There are no…

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Q: The population P (in thousands) of Tallahassee, Florida, from 2000 through 2018 can be modeled by P…

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Q: Suppose f(x, y) = (x - y) (25 - xy). Answer the following. Each answer should be a list of points…

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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: 1) fx²e-³x dx

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

Q: Graph the function hoo-x-30 0x30 30x50 0.5x-65 i x>50 Choose the correct graph below OA 1530456075…

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Q: Find the area of the shaded region. y 3 2 1 (1, 1) 2 y = ³x y || 4 1 X 6 X = 8 CO 8 X

A: Given equations of the curve

Q: A) Find the derivative of f(g(x)) at x=2  if f(2)=6, g(2)=3, f'(2)=1 and g'(2)= -2

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Q: In 1994, the moose population in a park was measured to be 4460. By 1997, the population was…

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Q: Express w as a linear combination of u and v. 4 --}-}--[:] W = 6 u 3 2 6 6

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Q: The following integral is an improper integral. ( Explain why it is improper, (b) determine whether…

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Q: 4. A water tank in the shape of an inverted cone has height 92 cm and radius 60 cm. If the water…

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Q: Let (a) (b) (√x + ²) dr + (y² + ln(2x)) dy=0, x>0. Check that this is an exact differential…

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Q: Find the marginal cost function. C(x) = 190 +5.7x-0.07x² c'(x) =

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Q: Use the definition of e, and numerical approximations as h approaches 0 from the left, and h…

A: Use the definition of e, and numerical approximation as h approaches 0 from the left and h…

Q: . D11: I can use derivatives to solve optimization problems. (a) Part of the graph of f(x) = x + 2x…

A: The given function is

Q: Let g(x) = 2x² - 216x. Find the relative maximum and minimum values of g. Also find the intervals on…

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Q: Use the differential for ex^(2)-y^2 to approximate the value of f(2.1,0.8). Your answer may have…

A: The given function isTo find,f(2.1, 0.8)

Q: Exponential Growth: a. The table below represents an exponential function. Find the missing values.…

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Q: Consider the graph of distances from the origin as a function of time for a car trip. 150 100 50…

A: This all the given problem by using the concept  slope of tangents at a point.

Q: y = (cos 7x)x

A: y=(cos⁡7x)x

Q: 3 + +++ -2 -3 -4 The graph above shows the base of an object. Compute the exact value of the volume…

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Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: The function is given byTo determine: The value of the second derivative of the function at point

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: ROBLEM No. 1. Solve the IVP: y"+6y-7y=0, subject to the initial conditions: y(0)=5; y '(0)= -3.

A: Given Differential equation is as follows

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: 3 11 (1 + ³²) ² lim (1+

A: L=limx→∞(1+3x)x11