1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x axis, the line x = 1, and the curve y=4-x².

Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

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Q: Find the solution of the given initial value problem: y (4) + 2y"+y = 3t+6; y(0) = y'(0) = 0, y" (0)…

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Q: A bank offers a 12% interest to be compounded annually. How much should a teacher deposit now if he…

A: A bank offers a 12% interest to be compounded annually. The teacher wants to receive Php. 15000 at…

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

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Q: b) Let f(x) = ¹. Find f'(x), ƒ"(x), ƒ"(x) and ƒ(4) (x). Deduce f(n)(x).

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Q: Write an equation for the function graphed below 13- 12- 1 - 5+ ++ -7 -6 -5 -4 -3 -2 -2 1-1 HE A 1 2…

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Q: Write an equation for the function graphed below -7 6 5 4 -3 -2 y= 50 on it'st 72 3 Q

A: Topic = Functions

Q: Find the TOTAL SOLUTION of the following Differential Equations: 1. 3 dy. dy +3 dt³ 2 dt² - 4 = 5t²…

A: Given the differential equation is d3ydt3 + 3d2ydt2 - 4 = 5t2 + 4

Q: Precalculus You have 5% and 20% but need to create 10% solution of 1,000 miligrams . How many…

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Q: 1. Find the orthogonal trajectory for the family of circles with center at (-2,3) and draw the…

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Q: 5. 6. Je*cos2x dx dx 3 (x+2)4 -(x + 2)2 S-

A: I have stated the used formulas in the solution

Q: A box without a lid is required to have volume, V = 32000 cm^3. Minimize the amount of cardboard…

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Q: 12 f(x) = x² - 6x² + 2 Determine the intervals on which f(x) is increasing/decreasing and identify…

A: Given,  f(x)=x125-6x25+2

Q: Evaluate the function at the given values of the Independent variable. Simplify the results. g(x) =…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: A white wine at room temperature 70° F is chilled in ice (32°F). If it takes 15 minutes for the wine…

A: *Differential equation model :- Newton's Law of heating.

Q: Vf(1, 3) =

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

A: We are asked to find the diminishing returns of the point.

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

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Q: Given that log a ( 2 ) = m and log a ( 3 ) = n , write exact expressions in terms of m and/or n for…

A: Write expression in terms of m and n for each of the following.

Q: all company of science writers found that its rate of profit (in thousands of dollars) after t years…

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Q: 1 Find the partial derivatives with respect to x for the function f(x,y) f = O O 9y³ x-y 9y3 (x-y)2…

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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: Two cars start from rest at a traffic light and accelerate for several minutes. The graph shows…

A: Given :The velocity of the graph of Car A and car B is given in the graph.And we know that the graph…

Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: The number of traffic accidents per year in a city of population p is predicted to be T 0.002p ³/2.…

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Q: 7. dx S- X-3√x²

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Write an equation for the function graphed below. The y intercept is at (0,0.3) 5+ 4- 3 5-4-3 1 1 2…

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Q: F(x, y, z) = -k At (-2,-2, -2) the vector is At (-2,-2, 2) the vector is At (-2, 2, -2) the vector…

A: Given vector field F(x,y,z)=-k Here k is constant

Q: Find an angle coterminal to  25π/3 that is between 0 and 2π

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Q: Evaluate using integration by parts: fx sec-¹x dx

A: SOLUTION-

Q: 2. Set up, but do not evaluate, the integral which gives the volume when the region bounded by the…

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Q: It was noon on a cold December day in Tampa: 16°C. Detective Taylor arrived at the crime scene to…

A: The solution is given below

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: VAI a. b. Given y =(x-2)²(3-x). Find the C. d. stationary points, interval of increasing and…

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Q: 1 if x > 0 x²-1 if x ≤0 g(x)=x-1

A: Given the function, gx=1x-1if x>0x2-1if x≤0

Q: A x Given that cosa= and 0 <a<, determine the exact value of cos 3 A cos = (Simplify your answer,…

A: All trigonometry ratio are positive in first quadrant .

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

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Q: Explain why the integral is improper. 100 1 10 X 1.4 converges diverges 1.2 1 y 0.8- 0.6 dx 0.4 0.2…

A: To find the value of an improper integral, convert the integral in terms of limits. If the resulting…

Q: I = √x f(x, y) dy dx-

A: ∫01∫0xf(x,y)dydx

Q: From the point (5,12,13) on the surface of g(x, y) = √x² + y², find the direction of maximum…

A: The gradient vector is a vector made up of all the partials of a given function. We compute it by…

Q: Evaluate the limits. If a limit does not exist, enter "DNE". You may use a GRAPH on Desmos or plot…

A: Here we have to use the concept of limit

Q: x = est, y = to (a) Find dw/dt by using the appropriate Chain Rule. dw dt W = X- (b) Find dw/dt by…

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Q: 10. (a) Construct the Taylor polynomial p3(x) of degree 3 for the function f(x) = 1/(2-x) around x =…

A: Solution is given below:

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

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Q: Find the radius of convergence and interval of convergence of the series n=1 (x - 5)n n5n

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Q: Use partial fractions to evaluate the following integral: x³ +6x²+3x+6 dx x³+2x²

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Q: thats a natural log of 9 to 0 and integral from 9 to e^x

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Q: Prove that the graph of the function y = x² −3+1/x has at least two x-intercepts in (0,2).

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