Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) B(u) = 3 tan¹(u) - u I

Q: Find the derivative of each of the following functions:-- log₂ x 2. y= X

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Q: Test the equation below for exactness. If exact, solve. If not, use an integrating factor (find it…

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Q: Q1/Without using L'Hopital rule, find the following limit. +². lim

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Q: 4. f 30x²5x³+3 dx e

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Q: Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral…

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Q: Find SS₁R³² z²dA where R = {(x, y) | 36x² +9y² ≤ 324}

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Q: 3 Jess bought a new car for £12 000. In the first year the value of the car depreciates by 20%. In…

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Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 25x² +…

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Q: -: Show that -1+i√3 =1 for all combination of signs.

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: A plane is defined by the equation x - 7y - 18z = 0. a. What is a normal vector to this plane? b.…

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Q: Evaluate +y² 1 Ez² + y² JJJ₁² dV, where E lies between the spheres z² + y² + 2² +2² 16 in the first…

A: Given that,

Q: 1. f(x) = 10 2. f(x) = 3 − 4x 1 2 3. f(x) = x² - 9x 2 4. f(x) = x² + 5x + 4 5. f(x) = 2 + 7x - 2x²

A: See the details solution in below

Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1

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Q: Find the distance between the points. (−14, 1), (1, −7)                     units

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Q: (f) The function f(x) = √√x is differentiable at x = 0. ○ True O False

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: y" - y' - y = cos(5t) - sin(5t); y(0) = 2 and y'=5

A: Given :y''-y'-y=cos5t-sin5ty(0)=2 and y'(0)=5

Q: 9-34 Evaluate the integral, if it exists. tb (1)nia 9. ² (8x³ + 3x²) dx 11. f' (1-x) dx 13. f³√x (x…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first part.

Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: The sum of two positive real numbers x and y is 12. Find an x and y among these such that the…

A: The sum of two positive real numbers x and y is 12.

Q: a. Find the Taylor polynomial of 6th order at a=- 2 b. Find error at x = π. X c. Graph the original…

A: To solve the following problem

Q: Evaluate the difference quotient f(a + h) - f(a) / h for the function f(x) = x ^ 2 + 4x - 5

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Q: 8. a. Using the vectors x = (3, 3, 1) and y = (-−1, 2, -3), verify that the following formula is…

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Q: Please explain this process: 49 7.760 Σ 7+1 10⁰ 49 = 3 1-7 3 10 ↑ n= P 16.33

A: Using geometry series

Q: Match the following functions with the appropriate cross-section: I) z = (y²-1) cos(x) II) z=(x²-1)…

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Q: A line segment has (x₁, y₁) as one endpoint and (xm, Ym) as its midpoint. Find the other endpoint…

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Q: Let R be & (t) = a vector based function defined loy < 1/2, 1, 0) if t = 1 3-√E 1-t² It cos nt if…

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Q: 2. Find the value of 1 3x + 13 x² + 4x +3 dx

A: We can you valve the given definite integral by using the partial fraction method.

Q: xy = 1, y = 0, x = 1, and x = 2 is rotated about the line x=-1.

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Q: 5. A ball of mass 2 kg is dropped from rest in a viscous fluid, the resistance of which is 0.001v N…

A: By solving differential equation

Q: Sketch the region of integration and change the order of integration. 4 [^ [V² F(x, y) dy dx 0 f(x,…

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Q: Prove that √1+i√3+√1-i√3 = √6

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Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: To find: Maximum profit

Q: Find dy dx 5. = sec ¹(log 7x) y =

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Q: All exponential functions can be written in many forms. Write the function ƒ(t) = 9600 (2) ³ in the…

A: We have to write the function in required form.

Q: 7. y - 5y + 7y" - 5y' + 6y = x² + 3x - 5 Ans: y = C₁e³x + C₂e²x + C3 cos x + C₁ sin x + x² + ²x -…

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

Q: 2. dx (x+1)√x-3

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Q: 3. What value of k will make the line with symmetric equations - (1,−1,3)+s(3,2,2) p vector equation…

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Q: Find the derivative of the function. <-2 g(x) = (7x² - - ² 4 4x + 7 g'(x) = 2 ((7x²-4) (28x²…

A: g(x)=7x2-44x+7-2 Chain rule: f(u(x))=f'(u(x))·u'(x)

Q: Use the given information to find A. A-1 [$3 4 5 5 12 NOTE: Write the elements of the matrix…

A: Topic = Matrix

Q: Which of the following statements is CORRECT? x³ + x 1 = 0 has no solution in [0, 2] Ox³ + x-1=0 has…

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Q: Q2/ Compute the following integral: 3 x √x - 4 dx

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Q: 5. Calculate the area of the parallelogram formed by the vectors (4, 10, 9) and (3, 1, -2).

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Q: The percentage of people of any particular age group that will die in a given year may be…

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Q: Ise the binomial series to find the Maclaurin series for the function. f(x) = √√1+x DO 1 x) = 1 + x…

A: To find the series expansion of following

Q: Find the derivative of the following function. -9e 5x y= 4x + 3 y'(x) =

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Q: b) The following incomplete y versus x data is given. X 1 2 6 7 5 11 ??? ??? 32 15 The data is fit…

A: Concept: The data given presents the value of y when x values are given That is when x=1 y=5means…

Q: You've been asked to calculate the mass of a conical pile of sawdust measuring 7 meters high with a…

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Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and ƒ'(0) = 8,…

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Q: magnitude of vector BC |BC| = magnitude of vector AB | A B|= angle A (using dot product) angle B…

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