Q/ Find the domain and range of the following functions メー」 y= 2y= メ+ 3+13 メー/3 3- 1,

Q: Find the centroid of the region bounded by the gi 1 y = 0, x = 1,x = 3 %3D %3D

A: Given:y=1/x ,y=0 ,x=1 and x=3 Find: the centroid of the region bounded by given curves.

Q: All parts of this problem refer to the function below. y = (9+ 6x)²/¤ dy a) Use logarithmic differen...

A: We have to find derivative

Q: Find dy/dx, if y=(x^2+2)^4 (2x−3)^5 dy/dx = _______

A:

Q: Below is the graph of y = x +5. 20- 15 10- -4 -3 -2 -1 0 1 The area bounded by y = x +5 and the raxi...

A: Given problem:- Find The area bounded by y= x2 +5 and the x-axis from  x=-3 to x = -1

Q: Calculating Mass from Radial Density. Mass-Density Formula of a Two-Dimensional Circular Object. Giv...

A: Given: m=∫0r2πxρxdx  ...(1) And ρx=6x ; x=6   We know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1 A...

Q: Find an equation of the tangent line to the curve y² = x³(3 – x) (a piriform) at the point (2,2/2). ...

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Q: Use a quick approximation to estimate the derivative of the given function at the indicated point. H...

A: We know that d/dx(xn)=nxn-1

Q: f (t) = 2 (sinh t) (sint)

A: The given function is: f(t)=2sinh(t) sin(t)

Q: 3sin4t dt 2. 5(1- 3cos21)

A: We have to find integral

Q: Setup the integral that will give the area of the surface generated by revolving the curve g(y) = 2/...

A: Given curve g(y)=24-yWe need to calculate the area of the surface generated by the curve g(y) over t...

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

A:

Q: f (t) = 7e – 2t sin(3t)

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Q: 3) y' dx-(xy+y*) dy-o Let the substitution v= i y vx; dy-vdx+xdv %3D )x*dy+(2xyy*) ax -o Let the sub...

A:

Q: Find the limit , if it exists:(Do not use L'Hospital's rule) 16 lim 2→16 16 Note: Give the exact ans...

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Q: 1. y'dx-(xy + y* \dy = 0 Let the substitution y=2; y= vx; dy=vdx+xdv

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Q: .A: The integral of the following function: In(sin² x) dx tan(x) ay be expressed as: A In®(sin x) + ...

A: Topic:- integration

Q: Bottled Water Sales The following chart shows annual per capita sales of bottled water in the United...

A:

Q: 4- y 2- 4 10 12 -2- -4 (a) I f (2) da = 10 (b) f (x) dx = 12 (c) A f(2) da = -5

A: To solve the following problem

Q: )ca) if vector as 6=2ナリーk Calculate axb and bxa. (b) Find The area of the paralletogrmais bounded by...

A: Area of parallelogram of the vectors a and b is a×b.

Q: Agree. Disagree 5. If lim f(x) # lim f(x), then lim f(x) does not exist. Justify:

A: Let's find. 

Q: d²y dy Solve: x2 dx2 + 3x+y = 4 cos (In x³) dx L: L:

A:

Q: Find the sum of the infinite series, if it exists. 1 1 6-1+ 36 6-1+-- t... Enter the sum as a fracti...

A: The general form of an infinite geometric series is: a + ar + ar2 + ar3 + ..... Here, a is the first...

Q: Question Evaluate the following limit using L'Hospital's rule. lim 3 In (x) 15х — 15 Provide an exac...

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Q: solve the second order differential equation ; y''+4y'+5y=8xsinx

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Q: Question 14 Which of the following is an equation of the parabola with the following properties: ver...

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Q: Determine the force due to hydrostatic pressure on a gate of an 8 ft tank filled with water (62.4 lb...

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Q: (In(x))? 3

A: We have to apply rules of integration to solve the problem

Q: Evaluate whether the following initial values is true in the function: y=4cos(x/2)+3x² a.) when x = ...

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Q: Find the limit lim 14,cos(, 18z Note: Give the exact answer but not the decimal approximation (for e...

A: Given:   limx→0+x14 ecosπ18x

Q: Finding the length of a curve. Arc length for y = f(x). Let f(x) be a smooth function over the inter...

A:

Q: Consider the following. f(x) = x* + 3 Find f'(x). f'(x) = Find the value of dy when x = -4 and dx = ...

A: f(x)= x4+3  Find 1) dy/dx  2) dy when x= -4 and dx= -0.01  3) ∆y when x= -4 and ∆x=-0.01 

Q: Solve the following second-order differential equation: y" + 4y/ + 5y = 8x sin x

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Q: Consider the graph of f(x) given below. (a) Analyzing the graph, if g(x) = f(æ), then g(x) is increa...

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Q: Consider the function f(x) = -6x2 + 4x – 6. (a) Find all critical numbers c of f. c= (b) The local m...

A: topic - application of derivatives

Q: Suppose Ris the region bounded above by the graph of f(z) = 1+ 6z – z² and below by the graph of g(z...

A: Given:     f(x) = 1+6x-x2       g(x) = 6/x

Q: 3sin4t di 5(1– 3cos21)

A: To solve the integration. 

Q: If the limit of a function f at x-3 equals -4, then which of the following are true?

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Q: Find the tangential and normal components of acceleration at the given time t for the plane curve r(...

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Q: zetch the region(s) enclosed by the given curves. Find the area oft y = r and y = VI 11

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Q: The demand function for a company's product is p 24e-0.99 where g is measured in thousands of units ...

A: Given: p=24e-0.9q  

Q: What is the equation of the directrix of the parabola X+2x+4y-27=0 2

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Q: raph of a function is given. y hich x in the range shown is the function increasing? For which x is ...

A: Given query is to find the interval of value of x where function is increasing and decreasing.

Q: 2メー7 f xス」

A:

Q: EVALUATE

A: ∫ x-3x-1+x2dx

Q: -3 -2 -1 1 2 3 g function is discontinuous at three values of x. List these values of t to largest. ...

A: Discontinouns

Q: What is the equation of the directrix of the parabola x2 + 2x+4y– 27=0? A y=8 B y=0 (© y= -2 D y=6

A: Solution ) x2 + 2x + 4y - 27 = 0 Add 1 and subtract 1 in equation  x2 + 2x +1  - 1  + 4y - 27 = 0 (x...

Q: Set up and evaluate the integral that gives the volume of the solid generated by revolving the plane...

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Q: Match each graph to its corresponding function. 1. f(x) = Væ graph in blue 2. g(x) = Vx – 2 graph in...

A: Answer: The solution is as given below : 

Q: Use the formula to calculate the balance A of an investment (in dollars) when P = $2,000, r = 4%, an...

A: Given:   A = 2000    r = 4% = 4/100 = 0.04     t = 10

Q: . The function f(x, y)= 8x' - /4x* + 3y* is homogenous in x and y of degree -. The function f(x, y)=...

A: Here we have to find the degree of homogeneous function