Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative derivative on (0,1).

Q: Without using a calculator, find the distance traveled by a particle with position (x, y) as t…

A: The distance travelled by the particle is the same as the arc length as varies within the interval…

Q: using an appropriate su OTE: Enter the exact answer. 4 | - | dx - 4 (1 – 2x) ¹ +C

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Q: The shape of a colony of bacteria on a Petri dish is circular. Find the approximate increase in its…

A: topic- application of derivatives

Q: Question 2 [2 Consider the matrix B= = (a (t -1 2 1 -1 2 1 -1 -2 0 Use the cofactor exapansion to…

A: We have to find the determinant.

Q: If f(2) = 5 and f ′(x) ≥ 2 for 2 ≤ x ≤ 7, how small can f(7) possibly be? f(7)

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Q: inction y = x ln (2x) articular solution for the nonhomogeneous differential equation xy" + xy - y =…

A: Topic:- differential equations Note :- as per our guideline if more than one question uploaded than…

Q: Let R be the region bounded by the curve y = 3√x and the line y = 3x. Then the double integral /…

A: Given problem:- Let R be the region bounded by the curve y = 3√x and the line y = 3x. Then the…

Q: Question 2 [" a. Find the critical points of the function f(x, y) = 6x² − 2x³ + 3y² + 6xy. b. s]…

A: Given :fx,y=6x2-2x3+3y2+6xy

Q: x² + y² - z² = 9 (u, v) = Determine the tangent plane at (3, 0, 0).

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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: Without using a calculator, for the following, determine whether the graph of the polar equation is…

A: Given that    r = 2 secθ            we know that    x(θ) =  r cosθ      and      y(θ) = r sinθ…

Q: Find an equation for the ellipse that satisfies the given conditions. Length of major axis: 10,…

A: NOTE: Refresh your page if you can't see any equations. . here foci n y-axis, which means the…

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

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Q: Evaluate the integral and check your answer by differen NOTE: Enter the exact answer. [x x(7+x²) dx…

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Q: Consider the function Question 1 f(x, y) = -y ln x + x lny + x y a) Find the directional derivative…

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Q: Find the angle between the vectors in radians and in degrees. (Round your answer for part (a) to…

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Q: Consider the following function and its graph. f(x): X x² + (b) Use the graph to determine the limit…

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Q: Find the limits. f(x) = x + 4 (a) (b) (c) g(x) = x² lim_ f(x) = X4-5 lim g(x): X-5 = lim g(f(x)) =

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Q: 4. Given x = 2 cos (6) and y = 2 sin(0), for 8 € [0, π] Eliminate the parameter to find a Cartesian…

A: Here, the given parametric equation is: x=2cos(θ), y=2sin(θ), for θ∈[0,2π]

Q: 2. Differentiate the following: (a) y = x²z

A: The given expression is: y=x2x   ...1   As we know the Product rule: f·g'=f'·g+f·g' The Power Law:…

Q: Find all relative extrema. Use the Second-Derivative Test where applicable. (If an answer does not…

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Q: Question Select one: 02 Evaluate 0-2 0 0 3 - 2n lim n→∞ 3 + n 0 3 O None of the others.

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Q: Given the region D in the first quadrant enclosed by x = 0, x = y², and y = 2. Express D as a region…

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Q: Find the lim inf (xn) and lim sup (x₂) of Xn = COS nπ

A: I have calculated the limits

Q: Solve the initial value problem y" - 3y' — 40y = 0, y(0) = a, y′(0) = −35. Find a so that the…

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Q: The values of two functions, f and g, are given in a table. One, both, or neither of them may be…

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Q: Question ( correct for the series 3): Which of the following is n=1 Select one: O equals. O equals…

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Q: Find the area under the graph of the function over the interval given. 1 √x [1,4] 25) y =

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Q: Use the given graph of f(x) to find the intervals on which f'(x) > 0. Q -5-4-3-2 25- 20- 15- 10- 5-…

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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: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) -8 (a) lim f(x) =…

A: To find out the limits.

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. -108 J-72 yz dx dz dy =

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Q: The value of the integral Select one: a. 2√2+1 3 b. None of these c. 2√2-1 3 2V/2 d. e 1 2 [²C x√√y…

A: Evaluating the definite integral

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) 6x²+x-1 6x²-3x -…

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Q: ·(2+ (2+x+31) dr by interpreting it in terms of areas. 9. Evaluate

A: Need to evaluate the integral by interpreting it in terms of areas. Given information; The integral…

Q: Evaluate the integral using an appropriate substitution. NOTE: Enter the exact answer. [e³ 34x dx =…

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Q: Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. X-2 9x - 4 f(x) =…

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Q: 14. Determine whether the triangles are similar. If they are, write a similarity statement. Explain…

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Q: Compute /16-³ dac

A: Solution of given question is written in below steps.

Q: 27. A function on [0,2] defined by f(x) = -x² |5x – 4 4x³ 3x (3x + 4 - if x ≤ 0 if 0 < x≤ 1 1<x<2 if…

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Q: = 0, y = x, and x = 5. n, the region D expressed as type I is: = {(x, y)|0 ≤ y ≤ x,0 ≤ x ≤ 5} ect…

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Q: Calculate fff(x, y, z) dS For s f(x, y, z) ds z² + y² = 16, 0≤ z ≤ 2; f(x, y, z)=e=²

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Q: Without using a calculator, sketch the parametric equations by eliminating the parameter. Indicate…

A: The given parametric equation x=4+2cosθ and y=-1+sinθ

Q: 10. Determine whether the series converges or diverges by using the integral test: Σnt n=1

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Q: 2²2 +2²2² = 12 25 (a) Find the vertices, foci, and eccentricity of the ellipse. (x, y) = (-5,0 (x,…

A: The equation is  x225+y29=1

Q: Maximum Profit Yaster Gadgets manufactures and sells a smartphones per week. The weekly price-demand…

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Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose…

A: This is a basic integration formula

Q: Find the derivative. F'(x) if F(x)= (ex¹ +5) 3 F'(x)=

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Q: divergent: Select one: O True False ts) The following series is 8 Σ6- n=1 3 n-2

A: Given: ∑n=1∞6-35n-2

Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: (2x, /, // ) (2x, -, -…

A: gradf =∇f =i∂∂x+j∂∂y+k∂∂zf .