Determine the integral by making the appropriate substitution. 1 2 x In 3x dx ⠀⠀

Q: Ĵ Refer to the graph shown below to evaluate -2 fit) f(t)dt.

A: A graph of the function  is given.The aim is to find the value of .The integral formula  is used in…

Q: (i) Find the area of the shaded region. 0 (1, 1) y=√√√2-x 2 x=y4

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Q: Use the graph to evaluate the limit. lim f(x) X→-1 X G

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Q: Suppose your newspaper is trying to decide between two competing desktop publishing software…

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Q: Write v as the sum of two vectors, one in Span {u₁) and one in Span (u₂,43,44). Assume that…

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 − x² −…

A: y=4−x2−ln⁡(12x+1), point (0,4)

Q: Given f"(x) = 9x - 1 and f'(0) = 5 and f(0) = -1. Find f'(x) = and find f(4) =

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Q: Use Newton's Method to find the third approximation -x3, for the root of f(x)= x^3-5x+1. Let x0= -3.

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Q: Use the table of values of f(0) = 0 f(0) -0.1 -7.6484 -0.01 99.7551 cos (70) 0 to estimate lim f(x),…

A: Limit does not exist when the left hand limit and right hand limit is not same.

Q: (4) Find the maximum and minimum values of f(x, y) = xy on the ellipse x² - xy + y² = 1.

A: The given equation of function  Let

Q: Evaluate the surface integral      SF · dS  for the given vector field F and the oriented surface…

A:

Q: f(x) = x² Which of the following is the linear approximation of f(x) at the point a=16? O O O 3…

A: f(x)=x3/8, a=16

Q: JO 1/8 ន √1 16x2 dx

A: By change of variables to evaluate the following definite integrals.

Q: 2. For the function g whose graph is shown, state the following. (b) lim g(x)= x-0 (a) lim g(x)=…

A: The graph of the function is given.The aim is to find the e)The equation of the vertical asymptotes.

Q: Determine the value of the following definite integral. St dz 15x+20x³ 3x²+2 Leave your answer in…

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Q: Find y'' if y=-8 cos x. OA. y'=8 sin x OB. y'= -8 cos x OC. y'= 8 cos x OD. y'= -8 sin x

A: Explaination of answer is as follows

Q: ate and classify all (by classifying the extrema, we mean listing whether locate any stationary…

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Q: 19 cookies, ho 10. The sum of three numbers is 161. The second number is 7 more than the first…

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Q: Find the unit tangent vector T(t) at point P. r(t) = t²i + tj + 20 k, T(5)= X P(25, 5, 20/3) Find a…

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Q: 8. Find the local maximum and minimum values and saddle point(s) of the function ● • f(x, y) =…

A: As per the company's guidelines, we are supposed to answer the first question for you, Kindly repost…

Q: (c) (d) (e) (f) YA -2 0 2 y = f(x) creasing? 4 6 8 x - [*11)dt g(x) = ) Does g(x) have any critical…

A: The graph of the function f(x) is shown as,It also given that,Note:"Since you have posted a question…

Q: Question 12 Determine the value of x(t) at t = 0 given its Laplace transform. Choose your answers…

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Q: (1) 2x2 + x- 5y2 = 4 2x2 + x + 5y2 = 4 3x²+1= 4y 12 (2) (3)

A: Note: As per our guidelines, we can solve the first three parts. Please repost the remaining sub…

Q: 1 Find an antiderivative F(x) with F'(x) = f(x) = -x and F(0) = 0. 3

A: F′(x)=f(x)=13x and F(0)=0

Q: Express in terms of logarithms without exponents. log(x³y4z)

A: Let,C=

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

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Q: 2. For f(x)=√14-2x (a). find the domain. Write your answer in interval notation. (b). Graph…

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Q: Which of the functions shown below is differentiable at x = -3? Select the correct answer below: O O…

A: The function non differentiable at iffunction is discontinuous at function has sharp/corner point…

Q: Evaluate the following indefinite and definite integrals using substitution.  Show all work, thank…

A: use substitution method for solving such integral

Q: The amount of carbon-14 present in animal bones t years after the animal's death is given by P(t) =…

A: The amount of carbon-14 present in animal bones t years after the animal's death is given…

Q: Find the indefinite integral. fett 7t dt = +C

A: I=∫e7tdt

Q: Find the average value of the function f(x)=√ x over the interval [0, 4]

A: f(x)=x over the interval [0,4]Average value of the function f(x) on [a,b] is given asfave…

Q: 6. Let So f(x) dx = 12, 5 Calculate the following integrals. (a) [°*3f(x)dx = (b) *2f(x) – g(x)dx =…

A: Let To calculate the following: (c) If  is an odd  function, then to find .Note:  Since, the student…

Q: The population of the world in 1987 was 5 billion and the continuous growth rate was estimated at…

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Q: Find a parametrization of the line in which the planes x+2y + 4z= -4 and 2x+3y +6z= -7 intersect.…

A: The given equations of planes are

Q: Find an antiderivative F(x) with F'(x) = f(x) = 6e² and F(0) = 4.

A: F′(x)=f(x)=6e2x and F(0)=4

Q: Draw the region whose area is given by the definite integral. (6-2 (6 - 2x)dx

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Q: Consider the graph of the function f below. What is the sign of the slope m of the tangent line at x…

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Q: A particular commodity has a price-demand equation given by p=√14,061 418x, where x is the amount in…

A: The price demand equation is given by  where x is the amount in pounds of the commodity demanded

Q: Use complex number operations to determine the solution to the expression below. The final solution…

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Q: 7. The area bounded by y = 2, y = -x², x = 1 and x = 2 equals A. 144 C. 3 B. D. 17 6 19 6

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Q: Find all the antiderivatives of the following function. Check your work by taking the derivative.…

A: Given,

Q: Write the given expression in an expanded form. Assume that variables represent positive numbers.…

A: Let

Q: Consider the problem min x2 + 2x2 such that r₁ + 2x₂ = 3 #1.22 The bordered Hessian for this problem…

A: The problem is given as,such that

Q: Give a geometric description of the set of points in space whose coordinates satisfy the given pair…

A: The given set is the set of points in space whose coordinates satisfy the pair of equations .The aim…

Q: Determine the integral using the substitution u = √√x+11. √(x +11) 1/2 √x+11 dx

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Q: Evaluate the following 2 j (x² + 3x-10) dx -5 √(x²+3x-10 +3x-10) dx = -5 (Type an exact answer. Use…

A: The given integral is .The aim is to find the value of the integral.Formula used:

Q: Find a, b, c, and d such that the curve ?=??3+??2+??+? has its tangent line at(1, 1) and at (0, -2)…

A: The objective of this question is to find the coefficients a, b, c, and d of the cubic function y =…

Q: Given the graph of f(x) below, find the graph of the derivative of f(x). Select the correct answer…

A: A graph of the function  is given.The aim is to sketch the graph of the derivative function.

Q: Evaluate each expression using the graphs of y = f(x) and y = g(x) shown below. a) (gof)(2) b)…

A: To evaluate each of the following expression by using the graphs of  shown below.