Assume that f (x) is differentiable functions for all x. Find the derivative of h(x) = x³. f(x).

Q: Determine whether the MVT applies to the given f on the given interval. Explain. If so, find all c…

A: Given function  f(x)=x3,           [-1,8]

Q: Find the local min, local max, and saddle points of the surfaces z = f(x,y) for the below function:…

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Q: 2x - 4 Find f ' (x) using the definition of the derivative: f ' (x) = lim h>0 f(x+h)-f(x) / h

A: Given query is to find the derivative using definition.

Q: Find the Wronskian of the given pair: e4t, e-3t/2 O (11/2)^(5/2) O -(11/2)^(5/2) O -(5/2)^(5/2) O…

A: e4t, e-3t/2

Q: 2. Use a calculator to evaluate the following expressions. Round your answer to 3 decimal places. a)…

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Q: How many local maxima does the function f(x) = 2x5 - 5x4 - 10x³ + 4 have? A] 4 [B] 3 [C] 0 [D] 2 [E]…

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Q: 2:27 A particle moves along the x-axis so that its > velocity at time 0 < t < 18 is given by v(t),…

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Q: What change of variables is suggested by an integral containing √x² +16? Choose the correct answer…

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Q: 1. We are interested in evaluating the integral 3 [√9-2² dr. Note that this integral gives you the…

A: Given: ∫039-x2dx a ) Let fx = 9-x2 Using Riemann sum with 3 rectangles and right-hand endpoints we…

Q: 5. Use Lagrange multipliers to find the extreme values of the f (x, y) = x² + 2y² subject to the…

A: By using Lagrange multipliers to find the extreme values of the function fx, y=x2+2y2 subject to the…

Q: The graph of f(x) = 4(x - 1)² - 4 is a parabola that opens upward ✔value of f. Need Help? Read It ✓…

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Q: 8. Find the directional derivative of f(x, y) direction of the point P to the point (4,1). = 2√x -…

A: directional derivative of f(x,y)=2x-y2 at the point P(1,5) in the direction of the point P to the…

Q: Use the e-6 definition of continuity to prove that the following functions are continuous at the…

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Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

A: we need to find out the directional derivative.

Q: which one of the following is the same as: -cos(-x)tan(-x) a. sinx b. -sinx c. -cotx

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Q: 2. 6-13x + 5x² 4. m¹m² - 12

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Q: Give the substitution that converts the given nonlinear equation into a linear equation then find…

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Q: Question 3 Find the transform of the given function by use of a table. f(t) = e4t 1 (A) F(s)= S + 4…

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Q: The auxiliary equation of y"" - 4y" - 4y' + 16y = 0 is r34r²4r + 16 = 0. The auxiliary equation has…

A: Given; f(r)=r3-4r2-4r+16 , [-0.75,3.75].

Q: A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t), whose…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. || y=…

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Q: Use the matrices below to perform matrix multiplication. B = 27 3] 14 -10 0 12 || |- 4 -3 5 10 6 8

A: Number of  column in B =3 = Number of Row  in   C  so, matrix multiplication is possible

Q: (a) In each of the following problems, you may assume that an exponential growth and decay model…

A: Solution: 2(a) (i) N0=200 g , N(t)=140 g, t=10 years

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1. sin(In 41x) X dx

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Q: Find the least squares regression line for the points. (0, 5), (3,

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Q: Determine the least possible degree of the polynomial function shown. The least possible degree…

A: We know that polynomial has degree n if it has n x intercept and polynomial has degree n if it has…

Q: Test each of the following equations for exactness and solve the equation. The equations that are…

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Q: The general solution to the DE in the initial value problem (IVP) 4 (y" + 6y' +9y = 0 y (0) = 1…

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Q: Johnson placed $15,000 into his credit union account paying 7% compounded semiannullay. How much…

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Q: Find the particular solution of the differential equation satisfying the initial conditions y(1) =…

A: Given differential equation:- x2y''+5xy'+13y=0

Q: 1. Evaluate the following expressions. Round your answer to 4 decimal places. a) 16 17 b) log,8. 195

A: Need to evaluate the given logarithmic expression.

Q: Find the transform of the given function by use of a table. f(t) = 5t sin (5t) + e-st cos (t) A…

A: Given : f(t) = 5t sin(5t) + e^(-5t) cos t

Q: If f(4) = 11, f'is continuous, and f(6) = Submit Answer fºt f'(x) dx = 19, what is the value of…

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Q: Find the equation of the tangent line to the function f(x) = 2x² - x at the point where X x = -1.…

A: Given query is to find the equation of the tangent line.

Q: f(x)=x²+2x-6 has an inverse g(x).. 1 ƒ'(g(x)) Use g '(x)= g'(-6)= 110 to find g '(-6).

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Q: Find y as a function of x if X y(0) = −1, y′(0) = 9, y″(0) y(x) = = -16. = y" - 4y" y + 4y = 0,

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Q: 2 3...... 2 y...) + Xdy =0 where yo...

A: Given differential equation  (2xy−1)dx+x2dy=0

Q: Suppose the revenue function for a product is given by the function:: R(q) = 7q2 + 14q where q is…

A: I am attaching image so that you understand each and every step.

Q: dy Find for the equation ex+y² = x. dx 3-x [A] [B] ³ xy 1-x 2xy [C] 1-2x xy [D] 2-x 2xy+e [E] 1-x xy

A: Concept: The formulas used: ddxxn=nxn-1ddxln(x)=1xln(ab)=bln(a)

Q: Find ff f(x, y) dA where f(x, y) = 3x + 1 and R= [0, 3] x [1,3]. R SSR f(x, y) dA =

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Q: Question Determine t' (x) if t(x) t'(x) t' (x) Select the correct answer below: = = Ɔ t'(x): ○ t'(x)…

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Q: Evaluate the following integral using partial fraction decomposition. S 12 (x-4)(x+8) 12 (x-4)(x+8)…

A: The given integral ∫12x-4x+8dx We have to find the integral using partial fraction.

Q: Find the linear approximation at x = 0 to show that the following commonly used approximations are…

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Q: F(s) = - A the in 3 B 55/2 S 3 -1/2 There is no correct answer from the given choices. D √₁ given…

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Q: the Wa Salve the... Following.. ......3x³6xy Ax (3x²+2 y.).dy. =a ... ... ... ... ..x 2y.). dy...…

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Q: -3x+6y = 9 x-2y = -3

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Q: 2. Write the formula for area of a circle: (a) Which two variables are related by this formula? (b)…

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Q: lim f(x) = 2-1 x²+x-2 x²-1

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Q: one has a Tess man its polynomial function. The volume of a cone is V = ²h for radius r and height…

A: Given query is to find the volume of the function.

Q: Chain Rule (One independent variable) Let z(x, y) = 2e* sin(y) where x = t' & y = 5mt. Calculate by…

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