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

Q: etermine whether the work done along the path C is positive, negative, or zero. O positive O…

A: To find the work done along the path c.

Q: Use the properties of infinite series to evaluate the following series. 3. 5" Σ n=0

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Q: In a display, there are 20 toys in the first row, 23 toys in the second row, and so on in an…

A: topic- arithmetic sequence

Q: (g°N)(x) (fºg)(x) If f(x)= x-1 and g(x)= x², what is the first derivative of (f+g)(x) (g-n(x) +

A: To find out the derivative of the indicated function.

Q: Question 5 A planning engineer for a new flour mill must present some estimates to his company…

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Q: Consider the following problem. Find the distance traveled In 15 seconds by an object traveling at a…

A: Given:          Velocity vt=20+6cost          time t=15 seconds We need to find the distance…

Q: You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person,…

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Q: 3. Divergent or convergent sequences. For each of the sequences below, enter either di- verges if…

A: Note : As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: f(x)=1/x-7 find an equation of the tangent line at the point (-2,-1/9)

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

A: The general form of a higher order linear differential equation is of the form f(D)y=Q(x). Where…

Q: Given the triangle not drawn to scale A = 16/ A 25 13 , find the measure of angle A using the Law of…

A: We can find the angle A using cosine rule as below.

Q: The directional derivative of f(x, y) = e²y - x at the point (1, 2) in the direction indicated by…

A: In this question, We want to find the directional derivative in the given direction.

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: Solve the differential equation by variation of parameters. 4x e2x y(x) = y" - 4y =

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Q: Obtain an exponential function in the form f(t) = Aet. HINT [See Example 5.] f(t) is the value after…

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Q: Simplify 8logg(64)

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Q: 6. 7. вне I' f(x)dx = 8. f(x)dx = [ f(x)dx= 3

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Q: Find the exact values of the six trigonometric ratios of the angle 8 in the triangle. sin(8) "…

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Q: Determine whether yp₂(x) = x is a particular solution of the following DE or not. y" + 4y = 4x.

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Q: Use the substitution method to solve the system -x+y=-2 4x - 3y = 9 Your answer is x= y =

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Q: Q1 (2 Let R be the region bounded by y = 0, y = x², x = 1. a) [ 1 Sketch the region R. b) Evaluate…

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Q: c) [ : Consider the series: 1 49 7-1+ 1 + i) Is the given series a geometric series? Explain. ii)…

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Q: 1. Evaluate the following: (ª) [e² (√π +6³) d dx

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Q: lim (In(x))/x

A: We use L'Hospital rule to evaluate the given limit.

Q: Find the marginal profit function if cost and revenue are given by C(x) = 157 +0.7x and R(x) = 8x…

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Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then…

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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: Which of the below double integrals has the following region? -1 5 4 3- 2 -1 0 Select one: None of…

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Q: Given the function h(x) below, select the answer choice(s) which correctly decompose h(x) into…

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Q: Lect one: True False

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Q: en differential equation by undetermined coef y = x²ex + + 3

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Q: c) Consider the series: 5-1+ 5 25 + .. i) Is the given series a geometric series? Explain. ii)…

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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: Question Determine the direction in which the graph of the following parabola opens. f(x)=(x-2)² – 5…

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Q: Solve the given initial-value problem. dx dt dy = 25x - y dt x(1) = 0, y(1) = 1 x(t) = 0 = -11x - y…

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Q: Consider the integral a = • 9₂ (y) 9₁ (y) 9₁(4) = f(x, y)dxdy b = 64 *** f(x, y) dyda. Sketch the…

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Q: Let V₁, V₂, and v3 be vectors in a vector space V, and let T:V R³ be a linear transformation for…

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Q: Which of the following functions is symmetric about the y-axis? f(x) = x2 f(x) = x3

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Q: Determine whether the following series converges or diverges. 2 9k +17 2 Σ k=11

A: Given Series   ∑k=1∞ 9k2+17k2To find: convergence or divergence of the series

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: 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: 1. Solve the differential equation: ² doc + 2xy = Inx, y (1) = 2

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Q: Find all point(s) on the graph ƒ (x) = √x³ + 5x + 1 that is(are) the closest to the point (5,0). A.…

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

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Q: L3Q15. Find (g/f) (x), if f(x) = x2 – 4 and g(x) = x – 2. A.x2 – x – 2 B.1/(x + 2)

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Q: L1Q16.Which of the following could be the end behavior of f(x) = -x6 + 3x4 + 8x3 – 4x2 – 6?   f(x) →…

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Q: Given the graph of ƒ' (x) below, where the Dom f (x) = (-∞, ∞). Find all INFLECTION point(s) of…

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Q: Choose the gradient of the function : f(x, y) = ex² Select one: O None of these ○ (6ye+²+³y², 2xer²…

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

A: Solved below.

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

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