Find the average value have of the function h on the given interval. h(u) = (9 — 6u)−¹, [−1,1]

Q: Graph the integrand and use areas to evaluate the integral. 5 S (5-1x) dx -5 A. 50 B. 75 C. 25 - 2…

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

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Q: Sketch the region enclosed by the given curves. 1 x, y = 4/x, y = 16x, y = 16 y 10 8 y 10+ Find its…

A: This question can be solved using the concept of area bounded by curves.

Q: D. (Bernoulli Differential Equation) Find the general (or particular) solution of the given…

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Q: Problem 2: The point P(0.5, 0) lies on the curve y = cos T.I. (a) If Q is the point (r, cos .r),…

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Q: ich of the following formulas would be used to calculate the trapezoid approximation of Jo 2x dx…

A: Topic:- application of integration

Q: Identify the rational function whose graph is given below. Note the x-intercept of the graph is a y…

A: topic:- function

Q: Sandy's main house is a hemispherical glass dome with diameter of 8m. Suppose that the glass is m…

A: NOTE: Refresh your page if you can't see any equations. . the diameter of the hemisphere is 8 m so…

Q: first-order

A: Given : y' = x9y + sin(x) The standard form of first order differential equation is  y' + p(x)*y =…

Q: nition 7.1.1. DEFINITION 7.1.1 Laplace Transform et f be a function defined for t > 0. Then the…

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Q: Problem #3: Consider the following statements. (1) Σ n=0 (-1)" 2n+1 X² (2n + 1)! = X- ∞ (iii) The…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

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Q: Example 6: Show that a a² 1 b b2 b c c2 Solution: L.H.S a a2 = = - (b - c) (c - a) (a - b) c 1 b b2…

A: Topic = Determinant

Q: Verify the Divergence Theorem by evaluating [/F. F. N ds as a surface integral and as a triple…

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Q: The points (-1,3) and (0,2) are on a curve and at any point (x, y) on the curve y" = 2-4x. Find the…

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Q: Consider the function below. 2²-2ry² + y² = 5 (a) Differentiate with respect to x (y is a function…

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Q: Tutorial Exercise Find the slope of the tangent line to the graph of the function at the given…

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Q: 8) Evaluate the following without the use of a calculator arccsc(-√2)

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 1 + est L{f(t)}

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Q: dy dx -5y=-tr, 5y = ³ 2 y(1)=1

A: The given differential equation is  dy/dx -5y= -5/2 xy3 , y(1)=1

Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.…

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Q: Find the derivative of the function. g(x) = [2 + (x² + 1)41³ g'(x) = 2 + (x8+ 4x6 + 6x² + 4x²+3)3

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Q: Find F(s). F(s) = £{t(et + e5t)2}

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Q: 6) Find the domain of the given functions (use interval notation) and the find f(g(x)) f(x) =…

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Q: If (x + 1) dx A B S + 2 (x + 2) (x - 1) ² = √ √(x + 2+ = -²1 A (B) O E 1 9 1 9 1 2 9 3 2 3 2/3 None…

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Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s²…

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Q: The tangent line to the graph of y = g(x) at the point (9, 1) passes through the point (4, 6). Find…

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Q: The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. 6 √x - 30 x - 25…

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Q: Complete the table by identifying u and du for the integral. [ f(g(x))g'(x) dx [x²√x² + 6 dx U= u =…

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Q: If k(x) 4 cos(x), then k'(x)

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Q: Find the limit. lim X-X lim X-8 sin 6x 5x sin 6x 5x = (Simplify your answer.)

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Q: Find the derivative of the following functions. F(x) = √²** 1. √/20162). 2. G(x) = 3. H(x) = L √t³ +…

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Q: Use spherical coordinates to find the volume of a ball with radius R(in other words, use spherical…

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Q: Graph the function given below by moving the vertical asymptote, then the value of the -intercept.…

A: Let's draw the graph.

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

A: The given data is: gy=8y To find: the volume of the solid obtained by rotating the region bounded on…

Q: In the following exercises, use direct substitution to show that each limit leads to the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Please explain how to solve, thank you!

A: Answer and explanation is given below.....

Q: The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 9,…

A: We have to find the 46th term of given sequence.

Q: Prove that: sec (0) +tan (0) cot (0)-cos (0) -=sec (0) tan (0)

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Q: Find the sum of the first 6 terms of the following series, to the nearest integer. 16, 32, 64,...

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Q: -10 -5 15 15 5 X 10

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Q: Write the first-order differential equation in standard form. (Use yp for y'.) −xy' = (8x + 7)y +…

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Q: What formula would be used to calculate the right rectangle approximation of ²(2x + 2)dx using five…

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Q: 19 a) Edur 1+2r 1 b) (1 +25), | E dr

A: We will solve  the integration.

Q: Consider the function f(x, y) = xe" and the point P(2,0). (a) Find a unit vector that gives the…

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

Q: Ise appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Two tourists with a surveying tool want to measure the distance from their hotel to the Washington…

A: Given data:- Distance from the Washington Monument to the Lincoln Memorial is 1.3 km From the…

Q: Find the total area enclosed between y = x³ and y = x over the interval [-1,9]. NOTE: Enter the…

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Q: For u(x, t) = f (x + ct) + g (x – ct), where c is a constant, find ux, ut, uxt . Show your work…

A: Given, u(x, t) = f (x + ct) + g (x – ct)