Use the functions below to find the given value. f(x) = x - 2 g(x) = x² | = (1)(₁_ 6+ z_ d)

Q: Use the gradient to find the directional derivative of the function at P in the direction of v. h(x,…

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Q: Evaluate the iterated integral. 2y 1²1,²% (10 + 8x² + 6y²) dx d 0 ly

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Q: At which of the following x-values does the function shown below have negative slope? Select all…

A: Given: From the above figure, we need to find x-values where the function has a negative slope. We…

Q: State the range of f(x)= {v=Ry>} b. ve Rly - } 3 a. 1 3x+4 C. {v=Ry>0} d. {ve Rly 0}

A: We can find the range as below.

Q: Evaluate the definite integral: f (x · cos(2x)) dx. Enter the exact decimal value. A graph of y = x…

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Q: 1) State the vertical asymptotes of f(x)= a. x=6₂x=-2 b. x=6, x=2 1 x² - 4x-12 c. d. x=-6, x=-2…

A: Given:         fx=1x2-4x-12 Vertical Asymptote:     For rational functions,the vertical asymptotes…

Q: 5. [tan³x sec³x dx

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Q: Consider the function in the graph to the right. The function has a Select an answer of at x = The…

A: Graph of the function is given.We have to find the increasing and decreasing interval and domain and…

Q: The graph below is the function f(x) -4 -3 -2 -1 8-1 lim 24-2 4 3 2 1 Determine the following…

A: Solution: As we can see in the graph

Q: - The complementary function is १ex . Ус where C₁, C₂, C3, C4 си the particular Solution se = c₁ex +…

A: This is a problem of ODE. Please follow the procedure given below.

Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4ex - 6 y(x) = 4

A: See this solution in below

Q: a. b. algal dy dx dy dx + y = xy³ - y = ex y² -X

A: See this solution in below.

Q: Find the general solution of the given second-order differential equation. 9y"+y' = 0 y(x) =

A: General solution of real roots is used.

Q: 2. The function ƒ(x) = x² − 4 is transformed to g(x) =— (x² − 4). Compare the domain, range,…

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Q: Use Properties of Exponents and Properties of Logarithms to simplify and the following expression…

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Q: Consider these three examples: A. S 1dx 1+x² B. f sin²x C.S.sin x dx We want to solve one using a…

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Q: For the function below, find a) the critical numbers; b) the open intervals where the function is…

A: The objective of the question is determine the critical point and intervals in which function is…

Q: Solve the given initial value problem. y" - 4y' + 3y = 0; y(0) = -1, The solution is y(t) = y'(0) =…

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Q: ∞ Determine whether the series (-1)-In -1/3 is absolutely convergent, conditionally conver- n=1

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Q: The profit from the sale of x units of radiators for automobiles and y units of radiators for…

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Q: Find the area bounded by y = x(x-1)^2, y = - 2 and the line x = A 10/3 = 2 B 5/3 C No of the options…

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Q: Write the expression in algebraic form. [Hint: Sketch a right triangle, as demonstrated In Example…

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Q: 2) Evaluate |x + 11 dx

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Q: 3 g-¹(x) = = (Write your inverse function in terms of the independent variable x.) Find the inverse…

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Q: Evaluate the line integral y = x² from (-1, 1) to (1, 1) and the line segment from (1, 1) to (−1,…

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Q: Find the real roots of the equation B 244

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Q: 3 Find the Cartesian coordinates of the following points (given in polar coordinates): 3.a (√2, π/4)…

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Q: Let f(x) = { tan^−1 ⁡(2x) if x ≥ 0, ax+b if x < 0. For which values of a and b is f(x)…

A: topic- limits and derivatives

Q: 1. Let r(0) = 2sin(0) + cos(Ⓒ) be the polar definition of a planar curve. Find, in standard x-y…

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Q: unction. Consider the function f, defined by: -1, f(x) = 2 500 0, 1, 2, Determine the exact value of…

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Q: 64 Use the first derivative test to answer the following: the function f(x) = 49x + I and a local…

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Q: 8. Calculate the following limits. In z lim → 2²-1 (b) [ 1³-1³ 0 e + cos2-1-2 lim

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Q: You go to the doctor and he gives you 14 milligrams of radioactive dye. After 12 minutes, 6.5…

A: Given ,  You go to the doctor and he gives you 14 milligrams of radioactive dye. After 12 minutes,…

Q: 2) Express 100C50 as a sum of two terms from Pascal's triangle.

A: Let us find thatThe  100C50 as a sum of two terms from Pascal's triangle.we know that the formula of…

Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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Q: Evaluate the integral. X √ ² ₁x + (x + 16y) dy

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Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: What is the gradient of f(x, y, z) = x³₂² + y³z +125z - 1 at P(5,5,-1) ? 75i + 75k -75i - 75k 75i -…

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Q: A population of rabbits oscillates 29 above and below an average of 75 during the year, hitting the…

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Q: Match the solution curve with one of the differential equations. f Ala Oy"+y=0 y" - 4y' - Sy=0 Oy" +…

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Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

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Q: Which of the following is the graph of y= sin (3x) for 0 ≤ x ≤ 6m?

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Q: Estimate the area under the graph of f(x) = approximating rectangles and right endpoints. R₁ = 1 x²…

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Q: at ch Use the Fundamental Theorem to show that the following is true. a f b C b [ f(x) dx = ff(x)dx…

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Q: 2. Given the function f(x, y)=3x²y + 2xy-y, a) find the value of the directional derivative of the…

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Q: The indicated function y₁(x) is a solution of the given differential equation. 6y"+y'- y = 0; y₁ =…

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Q: Using the circular disk method, find the volume of the solid generated by revolving about the…

A: Given curves , y=x ,                   (1)x=4.                       (2)

Q: 3 Solve the following ODES by Inverse Operator method 2 • (B³² +1) y = cos x 11

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Q: Diminishing Returns Jesaki Inc estimates that it will sell N(x) units of product after spending $x…

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Q: Solve the following ODES by Undetermined Coeff 11 4X y - 16 y = 19,2 € + 60e, y(a) = Y(u). 4X -4X…

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