The derivative of the function y=f(x) at the point x=c is characterized as the of the function at x=c. slope point of inflection O concavity O intercept

Q: point is OD. (Type an ordered triple.)

A: We are asked to find farthest point from sphere.

Q: Find the solution to the initial-value problem. y' = 3x2(y2 + 16), y(0) = 0 y =

A: Given:- y' = 3x2 (y2 + 16), y(0) = 0 To find:- The solution to the initial-value problem.

Q: 9. What is the slope of the curve at the given point? Sx² + 2.ry – y² = -3 at (.2)

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Q: Find the maximum and the minimum values of f(x,y,z) = 2x - 7y+7z on the sphere x² +y2 +z? = 102. ......

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Q: > A Moving to the next Question 2 dz Let z = 6e*v find O 12xy e**y O 18xy e**v O 18x*yex*y A Moving ...

A: Find the derivative

Q: An aquarium 7 m long, 3 m wide, and 4 m deep is full of water. Find the following: the hydrostatic p...

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Q: Question 18 tan(2x) Evaluate: lim x+o 2sin2(x) O a. 0 O b.-1 O C. 00 O d.-00

A: Given query is to find indicated limit.

Q: If r(5)=0, then which of following must be true? Olimf(x)=0 x+5 f(x)-f(5) -o lim x-5 X-5 fis continu...

A: Here we have given that  f'(5) = 0 We have to find which option is correct.

Q: The function f(x) sin(3x) has a Maclaurin series. Find the first 4 nonzero terms in the series, that...

A: Maclaurin series is just expansion of function with center zero. Which we xan found easily.

Q: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx) y = (tan x + sin...

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Q: initial-value

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Q: Let W = F(x , y , z) be a function such that Fx(0 , 0 , 0) = -1 , Fy(0 , 0 , O) = 3 , F2(0 ,0,0) = -...

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Q: If ƒ is continuous for a < x < b and differentiable for a < x < b , which of the following could be ...

A: Here, given that f is continuous for a≤x≤b and differentiable for a&lt;x&lt;b.

Q: Find the arc length of the space curve given by the vector function t3 i + t2 j + (2t + 1) k from th...

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Q: 1. The product of two numbers is 24. Find the numbers if (a) the sum of the two numbers is minimum, ...

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Q: 1. When is separation of variables applicable?

A: (1). . When is separation of variables applicable?

Q: Calculus Business Application Worksheet 1. A manufacturer makes fuel tanks for cars. The total weekl...

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Q: Solve the initial value problem. y' = (x − 1)(y − 3),  y(2) = 3 y =

A: To solve the initial value problem. 

Q: The Maclaurin series of the function f(x) = 9 cos(10z?) %3D can be written as f(x)= Cna" where a few...

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Q: In the quadratic equation Ax2+ Bx + C=0 describe the roots when 32 -4AC is negative. The roots are r...

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Q: whether the geom 08. (-7)" – 1 Σ 8" n = 1

A: Solution is given below:

Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of...

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Q: A depositor opens a new savings account with $5000 at 8% compounded semiannually. At the beginning o...

A: Let's find. 

Q: Using polar coordinates, find the area of the region shared by r=6cos(theta) and r=6sin(theta)

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Q: For the function f(x) = 5x° – 7x + 13x+ 3, find f'"(x). Then find f"(0) and f"(3). ... f"(x)= your c...

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Q: Find the general solution to the differential equation. dy dt = y cos(3t + 2) y =

A: We are given: dydt=y cos(3t+2) This can be solved as follows,

Q: Write the following expression in algebraic form: sin(arccos (6x)) V1-36z2 O VI – 36x² O VI – 6x² O ...

A: As per the company guidelines we can solve first question. I hope that the given solution will help ...

Q: Determine whether the series is convergent or divergent by expressing Sn as a telescoping sum. If it...

A: Determine whether the series is convergent or divergent by expressing Sn as a telescoping sum. If it...

Q: A ladder 20 feet long is placed against a wall. The foot of the ladder begins to slide away from the...

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Q: 교-3 with n5+3 Write an inequlity comparing for n 2 1. n3 (Express numbers in exact form. Use symboli...

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Q: of the function at x=c. The second derivative of the function y=f(x) at the point x=c is characteriz...

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Q: The graph of the equation 3x2 +2y2 +6x-16y+F=0 is either an ellipse, a point or an empty set. What s...

A: Equation of ellipse is (x-x1 ) 2 /a2+ ( y-y1)2/b2 =1

Q: 4. A rod is divided into ratio 1:3:5:6. If the 2nd to the shortest part is 35, find the length of th...

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Q: em #5: (a) Express the complex number (4-3/n) in the form a + bi. (b) Express the below complex numh...

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. nk - 1 k> 2 ...

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Q: ne region bounded by f(x) = - 1x + 7x + 18, = 0, and y O is rotated about the y-a ne volume of the s...

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Q: 2 Given f(x,y) = x?y-3xy³. Evaluate fdx 14y-27y + C 6. -6y3 + 8y/3+ C O 6x2 – 45x +C 4 2x2 – 12x+ C

A: ∫xn dx = xn+1n+1+C.

Q: Part a: Assume that the height of your cylinder is 4 inches. Consider A as a function of r, so we ca...

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Q: Find the critical numbers of f(z) = 2? – 18z + 4 and classify all extreme values given 0 < z < 12. a...

A: In this question we have to find the values of Critical nos. and absolute value of max and min.

Q: Find the general solution to the differential equation. y' = 6xy2 y

A: The given differential equation,         y'=6xy2

Q: 2e" dx (e® – 1)2 1

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Q: Given the series 3" Σ n=1 antl find the ratio an (Express numbers in exact form. Use symbolic notati...

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Q: Write a chain rule formula for the following derivative. aw for w = f(x, y, z); x = g(r, s, t), y = ...

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Q: A space probe in the shape of the ellipsoid 16x +y + 4z = 20 enters a planet's atmosphere and its su...

A: According to guidelines we solve only first question. 

Q: Find an LU decomposition for the coefficient matrix and hence solve the system of equations xị -2x2 ...

A: We can write the given equation as:  1-231-121-13-613x1x2x3=7-313 The coefficient matrix is: A=1-231...

Q: Given f (x) = sin x and g (x) = cos x, show that f (g (5)) = 0. Show all your %3| steps.

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Q: d²y dx dy =-9y+ 7e³* + A 3x 6. dx

A: Topic:- differential equations

Q: 1.) Explain why the integral below is an improper integral and what two integrals tell us whether it...

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Q: s the area of the shaded region equal to the area of unshaded shaded?

A: Yes, Area will be equal of shaded region and unshaded region.

Q: The following three lines do not have a common intersection: x + y = 2, x – y = 5 and x + 2y = 6. Ho...

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