Differentiate. f(x) = In f'(x) = : 100

Q: Differentiate the function. y' = y = (In(1 + e*))5

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Q: Find the length of the following two-dimensional curve. r(t) = (201² - 2,48t² + 3), for 0 ≤t≤ 1

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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: Given F(1) = 1, F'(1) = 1, F(2) = 3, F'(2) = 7 and G(2) = 1, G′(2) = 5, G(3) = 6, G′(3) = 2, find…

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Q: 5. Find the equation of the ellipse with center at (4, 4), vertices at (4, 10) and (4, -2), foci at…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Use implicit differentiation to find 있으 9 sin (xy) = 8x + 5y = dy dx

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

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: 6. Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on…

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Q: Vector w has initial point (2, -1, 3) and terminal point (-4, 75). Which of the following vectors is…

A: Vector  has initial point  and terminal point . To find the vector which is parallel to .

Q: Calculate the determinant of A = [³] 55 det (A) = Number

A: Given, If , than

Q: 4. A = -1 0 5-2 245 0 -3 , B= 7 650 -3 -4 2 -1,c=7,d=5 7 9

A: we are given the matrices and we need to find out the matrix cA+dB

Q: Evaluate and simplify y'. 5x²-9x 2 3x+4 y=- y'=0

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Q: Find f. f"(x) = -2 + 36x - 12x2, f(0) = 2, f'(0) = 18

A: Given, .Given,  f(0)=2, f'(0)=18.We know,

Q: = (a) Draw the exponential function: y 3x Also identify the asymptote to this function in your…

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Q: Find dy/dx by implicit differentiation. 9 cos(x) sin(y) = 1 dy dx

A: Given, 9cos(x)sin(y)=1.we know,

Q: (i) (k) dx (tan x) dx (secx) = = (j) (cscx) = dx (1) :(cotx) = =

A: As per your request, we answer only parts (j) , (k) and (l).find using derivative rules

Q: Set up the definite integral required to find the area of the region between the graph of y = 16 -…

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Q: Find the eigenvalue associated with the eigenvector A = Number -[-28] = of the matrix A=

A: The given eigenvector is The given matrix is

Q: Find dy clx In (sin(8x3)) a) y=(√√x2-1) In (sin( b) y = 1+ sin ² (3x)+sin 4 (3x) + sin 6 (3x)+.... +…

A: Since, you have posted multiple questions.As per guidelines we are supposed to answer only first…

Q: Find the GCF of the expressions. 15a8b(c – 7) and 12a¹⁰b7(7 — c)

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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: Find the area between the curves. y=x2 − 9x + 3  and  y=x2 + 9  from  x=0  to  x=6

A: The region between the curves  from The graph of region

Q: Find the first partial derivatives of the following function. f(x,y) = 3xy³ + 1 =

A: By treating one variable at a time and other as a constant, we can find the partial derivative.

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: 4. Find the following limits. If the li -∞0, write that. (a) e³x-1 lim x→0 5x

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

Q: f(x)=x54x

A: Given that functionWe have to find the derivative of the given function

Q: 2. For what values of n does this integral converge or diverge? Show all evidentiary work for each…

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Q: 2. Find a function f such that f'(x)= xf(x)-x and f(0) = 2.

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Q: If t(x)=0.9exln(x), find t′(5) to the nearest tenth

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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: Solve the equation and check your solution. 5x − 14 3 X = 15+X -2 +4

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Q: Set up the definite integral required to find the area of the region between the graph of y = x² -…

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Q: Given an acceleration vector, initial velocity (uovo,wo), and initial position (xo.YoZo), find the…

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Q: A particle is moving with the given data. Find the position of the particle. a(t) t²8t +4, s(0)= 0,…

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Q: Given: x=t², y=t-8, -4≤t≤4 a) Sketch the curve by using the parametric equations to plot points.…

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Q: For the polynomial, determine its standard form, degree, coefficients, leading coefficient, and…

A: Given:- 5x + x4 - 3Standard Form is given by Standard form :- x4 + 5x - 3

Q: 3. A particle moves according to a law of motion s = where t is measured in seconds and s is…

A: Given:

Q: Differentiate. y = In (4x² - 7x+5) y' =0

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Q: Inx 2. Let f be the function given by f(x) = for all x > 0. The derivative offis given by 1- ln x…

A: The given function is; f(x)=lnx/x

Q: Set up, but do not evaluate, an integral for area of the surface obtained by rotating the curve…

A: To set up, but not to evaluate, an integral for the area of the surface obtained by rotatng the…

Q: Use the differential dy to approximate 4y when x changes from x = 2 to x = 1.96. y = X x² + 1 Enter…

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Q: 8. Find the derivative of each. N (a) y = sin-¹(x³)

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

Q: A spherical tank with a radius of 3 meters is half-full sitting on the ground. Set up an integral…

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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: 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: = Let F be the vector field F(x, y, z) = xi+yj +4zk √²+2 beneath the plane = = 3, oriented using a…

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Q: Given F(1) = 1, F'(1) = 1, F(2) = 3, F'(2) = 7 and G(2) = 1, G'(2) = 5, G(3) = 6, G'(3) = 2, find…

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Q: Find the total differential d2 for the dx = 0.01 X= 2 Y = 0 and dy = 0.01 J2 and 42 LE of function…

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Q: For any two nonparallel vectors a and b, it holds that Select one: O 3a + b 3|a| + |b| O|3a + b =…

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Q: Suppose z = x² sin y, a = 48² t², y= 8st. A. Use the chain rule to find and all x, y, s and t in…

A: z=x2-t2 ,y=8st