Evaluate the integral and check your answer by differentiating. x² +8x4 1 x6 1² dx +C

Q: Create a table of values for the function and use the result to estimate the limit. Use a graphing…

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Q: L4Q10.The first term of an arithmetic sequence is 11 and the second term is 16. Find the common…

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Q: A machinist is required to manufacture a circular metal disk with area 588 cm². Give your answers in…

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Q: Solve the following equation. [Hint: Change log 16x and log 4x to base 2.] log 16x + log 4x + log2x…

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Q: 1 = x², x = 1 Given the region D in R2 enclosed by Sketch the region D Compute the iterated double…

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Q: (a) Find the area of the region bounded by the given curves I + y = 0, r = y² + 3y. (b) Let R be the…

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Q: What is the area of the right triangle with vertices at P(4,3 6), Q(-2. 0, 8) and R(1, 5, 0) ? O…

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Q: Let f(x, y) = 3x² + 2y² − 2xy — 1. Find the local maximum and minimum values and saddle points of f,…

A: Double integral, Maxima minima

Q: Suppose (1, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: As we know from the double differentiability test, When rt-s2>0 and r>0 then minima will…

Q: What is the distance between the given pla P₁: z=x+2y + 1 P2: 3x + 6y-3z = 4 O 0.95 O 1.50 O 0.14

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Q: The double integral √ √ ₁ (3. R (3x² + 2y), where R = [1, 2] × [-1, 2] is equal to Select one: O 18…

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Q: 1. Find the gradient of the function f(x, y) = x² sin y.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Give an example of a derivable function f (x) with f ′ (- 4) = - 1

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Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

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Q: (a) Find the area of the region bounded by the given curves a x = e.

A: Solved below.

Q: Question 1 enclosed by Given the region D in R² y = 0, y = 1, x = 0, x = y² a. b. [ integral Sketch…

A: Given :- y=0,y=1,x=0 and x=y2 To find:- Sketch the region D Compute ∫01∫0y23y3exydxdy

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: 1. Find the critical points of the function 2 f(x, y) = x² + 4xy.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the derivative of the function f(z) = √2 O None of these. 37 Of(z) = √2z f(2)=

A: We will find the derivative.

Q: Find the derivative of the function f(x) = (3x² – 2x³ O f'(x) = (12x³ - 6x²) ³/2 f'(x) = O 3 f'(x)=…

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Q: Simplify 8logg(64)

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Q: 4. Which of the following differential equations has the slope field below 22 ܟ O dy dx dx dx ܔܔܔ…

A: The given slope field is for dydx = -xy . Because slope y'(x) of the solution y(x) is determined…

Q: Find the area of the triangle. (Round your answer to one decimal place.) 2

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Q: 9. Find if x (t) = t + sin(t), and y(t) = t - cos(t). doe

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Q: When demonstrating that lim 5x + 3 = 8 with = 0.3, which of the following 8-values suffices? x →1 08…

A: limx→15x+3=8 with ε=0.3 We have to find the δ value.

Q: Find the work done by the force field F on a particle moving along the given path. F(x, y) = xi +…

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Q: 68t ²+2 An epidemic is growing in a region according to the rate N'(t) = 1 where N(t) is the number…

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Q: Solve the following equation. [Hint: Change log 4x to base 2.] log2 (x+4) - log 4x=2

A: To solve the equation.

Q: L1Q7. If the degree of a polynomial function is odd and the leading coefficient is negative, then…

A: We can solve as follows

Q: Evaluate the integral 0 2 0 2-x xdydx.

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Q: Question 5 (a) Find an equation of the curve that passes through the point (0, -2) and whose slope…

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Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy…

A: Gievn, x=4t,y=8t And 0≤t≤1

Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to <2,1>

Q: Find the general indefinite integral. (Use C for the constant of integration.) Sax ⁹⁹ .99 ax ⁹⁹ +…

A: As per our guidelines we only solve one question (1st question) and rest of the question will be…

Q: Model the data using an exponential function f(x) = Abx. f(x) = = X f(x) 0: 1 2 300 90 27

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Q: Evaluate 112x (2x - y) dx + (x + 3y) dy. C: x-axis from x = 0 to x = 6

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Q: The equation of the tangent plane to the surface x² z² at the point (-2, 1, 3) is Select one: + 2y.…

A: To find the equation of tangent plane.

Q: Find the volume of the given solid region in the first octant bounded by the plane 10x + 8y +20z =…

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Q: ether yp₂ (x) = x is a particular solution g DE or not. y" + 4y = 4x.

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Q: Find the slope and y-Intercept (if possible) of the line. (If an answer is undefined, enter…

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Q: Use the double integration find the area of the parallelogram whose vertices are A(1,0), B(3,1),…

A: Area of parallelogram

Q: Given f(-6)= 18, f'(-6) = -16, g(-6) = -10, and g' (-6) = 14, find the value of h' (-6) based on the…

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Q: Model the data using an exponential function f(x) = Ab×. f(x) = = X f(x) 0 1 25 15 2 9

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Q: ⁹1 9x + 7 8x5 dx || +C

A: Given: ∫9x+78x5dx

Q: Is the equality T ["(" true or false? Select one: O True O False 8r sin 0 dr d0 = 0

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Q: but

A: Please refer to the image below

Q: Find f'(x). f(x)= ex+ 5x 3 Inx f'(x) =

A: We have to find the derivative.

Q: Simplify

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Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. [t√4 t√4t² +…

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