Differentiate. f(x)= x³ In 7x 3 f'(x) =

Q: Evaluate the integral by reversing the order of integration. 1 1₁² X 4 y³ + 1 dy dx

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Q: Find the length of the parabolic segment r = 14 1 + cos 0 The length is (Type an exact answer, using…

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Q: A table of values for f, g, f', and g' is given. g(x) 2 8 2 Xx 1 2 3 f(x) 3 1 7 (a) If h(x) =…

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Q: alculate the derivative of the following function. y = (p+e)5 sin p³ 3 ***

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Q: 6 Use the following methods to estimate fdx: X 2 a. Left endpoint approximation L 3 b. Trapezoidal…

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Q: Suppose the amount of caffeine (in mg) in a person's body t hours after consuming it is C(t) = 75…

A: Suppose the amount of caffeine (in mg) in a person's body t hours after consuming it isTo compute…

Q: How did you get (xe^x - integral ( e^x dx)?

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Q: Evaluate the definite integral. re4 dx 1 x√In x

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Q: Determine the point(s) at which the graph of the function f(x)= horizontal tangent line (when f'(x)…

A: The given function is

Q: Find and simplify the derivative of the following function. f(x) = 25xe x -X The derivative of f(x)…

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Q: Given F(r, s, t) = -r (3s5 + 6t5), compute: Frst

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Q: 1. Let f be the function defined by f(x) = ln(2+ sin x) for ≤x≤2. a) Find the absolute maximum and…

A: The given function  for .The aim is to find the absolute extreme values and the inflection points.

Q: Student's Homework Problem Evaluate the integral. J cos (ln(3x)) dx Student's Solution. 1 cos…

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Q: Write a polynomial f(x) that satisfies the given conditions. Degree 3 polynomial with integer…

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Q: Find the equation (in terms of 2) of the line through the points (-4,-2) and (4,2) Y

A: Find an equation of the line pass through (-4,-2) and (4,2)

Q: 1. Match the rule or formula's name with its characteristics by putting the lowercase letter on the…

A: Consider the following

Q: K What is the slope of the line tangent to the graph of y=tan(-x) at x = - 4? The slope of the…

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Q: Find the partial derivatives of the function B || || w = √3r² +8s² + 6t²

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Q: How do I prove, |3- x/3| 9 (1 - x/3x)=-2

A: If is a function and then we say  if for any  there is  such that .

Q: F'(x) = f(x) = 4x5-35x² + 40x Compare the graphs of f and f' and use them to explain why your answer…

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = x5 e-x (a) Find the…

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Q: Inx for all x > 0. The derivative of fis given by x 2. Let f be the function given by f(x) = f'(x)=-…

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Q: Calculate the derivative of the following functions. 15 (a) f(x) = (1) f'(x) = (b) y = dy dt h'(y) =…

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Q: (a) ㎡(c) = = (x) (9)

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

Q: Find the maximum rate of change of f(x, y, z) = x+y/z at the point (3, 4, 5) and the direction in…

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Q: Let A be a 2 x 3 matrix and T: R³ → R² be the linear mapping T (7) = A 7. 2 (6) - A) ¹ (1) - ()-[²]…

A: Consider the linear transformation

Q: Find the partial derivatives of the function fz(x, y) fy(x, y) = fry (x, y) = fyz(x, y) = f(x, y) =…

A: Given,

Q: ㅐㅍ 3 1/2 S (2+4C05(0)) ² do 2 싫어

A: To evaluate the following integral.

Q: 4. A = [ 5 7 5 ²]. b = = ['₁ 5 12 17

A: Given,

Q: Find an equation of the ellipse with the following characteristics, assuming the center is at the…

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Q: Determine the derivative of the following function with respect to a: 75 +¹rsin (r) 4,

A: f(x)=π5+π4xsin⁡(x)

Q: -4-3 4 3 2 1 -1- -2 -3- 1 f(x) 2 3 X g(x) 4 5

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Q: Application of De A tank contains 1,200 liters of fresh water. Brine containing 0.2 kg/liter of salt…

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Q: Q8 Find the set of intervals for the following functions (a) f (x) > 0 (b) f(x) = 0 (a) f(x) < 0 (b)…

A: we are given graphs of wo functions and we are to find on what intervals are those functions…

Q: Answer the following questions for the function f(x)=x√x² + 16 defined on the interval -6 ≤ x ≤ 6.…

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Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (5, 5) in the direction = 3/4…

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Q: Find the length and direction of u x v. u=4i+2j+8k, v=-i-2j-2k

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Q: 11. A conical water tank with a vertex angle of 60° is being filled with water at a constant rate of…

A: Let r be the radius of the water surface and h be the height of the water inside the cone at any…

Q: Find the intersection of the line x = -1 + 2t, y = 3 + t, z = 4 - t with the yz-plane. O (1, -3, -4)…

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Q: 5x+500 A garden shop determines the demand function q = D(x) = 20x +9 the number of plants sold per…

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Q: 5. Recall that y = sec-¹x (with domain x ≥ 1) means sec y=x and 0 ≤y</2 or T ≤ y ≤ 37/2. Use…

A: To prove

Q: Write the given expression as a SINGLE logarithmic term. log(x + 6) - / log(x + 3) + log(x - 1), x>…

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Q: Problem 2: Use Cramer's Rule to solve for the System of Equations by hand: -x + y = 10 5x + 4y = 2

A: By using Cramer's Rule to solve the following system of equations.

Q: Consider the following. (If an answer does not exist, enter DNE.) 32 +² (a) Find the interval(s) on…

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Q: Find the length of the indicated portion of the curve by first finding the arc length parameter…

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Q: The continuous compound interest formula is given by A = Pert where A is the accumulated amount,…

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Q: The curve of a function f (x) is given in the figure below and you are asked to draw on it   a)…

A: The curve of the function f(x) is shown as,

Q: Use the chain rule to find and where First the pieces: 8/8 8/3 3/5 |||||| || ||||70 And putting it…

A: Consider

Q: Problem 3 Find the areas of the following regions contained in the (x, y)-plane. (1) R = {(x,y) :…

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Q: Find the derivative of the function. y = sin¯¹(cos¹(t)) y' =

A: Given that expression we have to find the value of