Find and simplify the derivative of f(x) = ln(cosh (ax))

Q: LATIHAN 1 1. Obtain the cartesian equation of the curve by eliminating the parameter a. x = 3t ; y =…

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Q: (a) Find the equation of the tangent line to the curve y = x² at x = 1. (b) The line in part (a) is…

A: Let m be the derivative of y w.r.t x at the given point x, then the slope is m. The equation of the…

Q: In order to approximate the area under f(x) = e²² from x = 5 to x = 22 using 20 rectangles and the…

A: We need to approximate the area under f(x)=e-x2 from x=5 to x=22. So, here, a=5 and b=22.

Q: In 1997, researchers at Texas A&M University estimated the operating costs of c sizes. A quadratic…

A: Given: c(q)=0.021q2+26.9q+313

Q: Use row reduction to find the inverse of the given matrix if it exists, and check your answer by…

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Q: 3. Use the Root Test or the Ratio Test to determine whether the series is absolutely convergent,…

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Q: Given f(x) = ln(3x2 + 8x + 2), find the equation of the line tangent to the graph of f at x = 0.

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Q: Show that the lines L₁ : x = 3-t, y = 2t, z = 2+t and L₂: x = 1 + 4t, y = 3-8t, z = 5 - 4t are…

A: Solution is given below:

Q: The cost of manufacturing x electric woks in one day is given by C (x) = 2x³ – 16x² + 4x and the…

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Q: "This passcode consists of the two below limits which include an Remember to type "infinity" for 0,…

A: For x approaching c from the left, x<c  ⇒  x-c5<0The denominator is a negative  approaching…

Q: Verify that the given differential equation is exact, then solve it. 10x 24y 16y 5x (3) dx + X y 4 X…

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Q: Find an equation of the tangent line to the graph of the given function at the specified point. x²-1…

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Q: Find the distance x = 2 + 6t, y x = 9-t, NOTE: Enter the exact answer. D = [ between the skew lines:…

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Q: Find the area of the parallelogram with vertices A(-5, 5), B(−3, 8), C(1, 6), and D(-1, 3).

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Q: Find the elasticity of demand (E) for the given demand function at the indicated values of p. Is the…

A: The given demand function is: g=408-0.3p

Q: (a) The curve with equation y2 = 5x4 - x2 is called a kampyle of Eudoxus. Find an equation of the…

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Q: Suppose that f is a function given as f(x) = -3x² - 2x - 3. Simplify the expression f(x + h). f(x +…

A: f(x)=-3x2-2x-3(i) f(x+h)=-3(x+h)2-2(x+h)-3

Q: Refer to the following figure, which displays a right circular cone along with the formulas for the…

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Q: 4. Find the exact arc length of the curve over the stated interval: x=3t², y=t³,0 ≤t≤2

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Q: (3) Evaluate the slope of the tangent line for the graph of the x2 x²+1 at x = 1 function h(x) =

A: The given function is: hx=x2x+1  To find the slope of the tangent line at x=1

Q: A) 77. Shown above is a slope field for which of the following differential equations? dy x-y dx y…

A: The answer is in step2.

Q: Suppose f(x,y)=xy(1−10x−4y). f(x,y) has 4 critical points. List them in increasing lexographic…

A: We can solve the given problem by using the second derivative test.

Q: For all sets A, B, and C, we have the identity Ax (B-C) = (A x B)-(A x C). . Use element chasing to…

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Q: What is the minimum value of f(x) = x^2 - 8 ln x   on the interval [1,5]

A: To determine the minimum value of fx=x2-8 lnx on the interval 1, 5.

Q: Find the distance between the skew lines: x = 2 + 6t, y = 1+ 2t, z = 1 - 4t x = 3-t, y = 9, 2 = 4 +…

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Q: Find the cross product a x b. a =j + 6k, b = 5i - j + 4k Verify that it is orthogonal to both a and…

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Q: aluate the limit lim x→1 ƒ(x)-ƒ(1) x-1 using the limit toolkit developed in class

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Q: Find the inflection points of f(x) = x¹ + 9x³ — 15x² + 15. (

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Q: Express the given parametric equations of a line using bracket notation and also using i, j, k…

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Q: Find the length of the vector. v = (4, 0, -2,-5) ||v|| =

A: v=(4,0,-2,-5)

Q: Let P(x) = F(x)G(x) and Q(x) 7 (a) Find P'(2). (b) Find Q'(7). y 15 + 3 2 1 - = N F(x) G(x) 3 where…

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Q: Estimate the area under the graph of F(X)=X2 +6X+11  over the interval [0,8] using four…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The region bounded by x=y and x = √y is rotated about the line y = -2. Which of the following would…

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Q: Find the compound amount and the amount of interest earned by the following deposit. $9,000 at…

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Q: The region Rin the first quadrant is enclosed by the lines x=0 and y=5 and the graph of y = x² + 1.…

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Q: In a trend that scientists attribute, at least part, to global warming, a certain floating cap of…

A: We have to find the rate of change of area.

Q: A 13 foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

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Q: Use calculus to find the area A of the triangle with the given vertices. (0, 0), (5, 3), (1,8)

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Q: Find the open interval(s) where the function is decreasing. f(x) = (x + 1)/(x - 4) typed answer…

A: Given that , f(x)=x+1x-4To determine an open interval where f is decreasing. The function f is…

Q: Find the derivative of g(x) = x² ex

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Q: A drug is administered to a patient through an IV drip. The drug concentration (in milligrams/…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: Find parametric equations of the line that satisfies the stated conditions. The line that is tangent…

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Q: Evaluate the given expression. Take 0-2 40-0 and C = 1 4A + 0.5C P 1 1 -1

A: We have given A=0-2-2021 and c=1-111-1-1

Q: Find the derivative of the function at the given number. f(x) = √x at 25 f'(25) =

A: To find the derivative of the function at the given number. fx=x at 25

Q: y=2x R y=x²

A: To write an iterated integral for ∫R∫dA over the region R described  in the figure below. (a)…

Q: 2. Use integration in cylindrical coordinates in order to compute the vol- ume of: U = {(x, y, z) :…

A: We have to use cylindrical coordinates in order to find the volume of thegiven region.

Q: The passcode for this gate is found by determining the domain of the derivative of f(x) and 45 then…

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Q: Find the value of the summation. Σ( – 3) - k 0

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Q: Find the point of intersection (xo, Yo, Zo) of the lines given as: L₁: L₂: Xo = Yo = Zo = M i x=…

A: Given lines equation:- L1: x=3+t,y=5+6t,z=5+tL2: x=3+t, y=6+7t,z=6+2t