Express the following functions in terms of function f where y=f(x). Professor Lapan's Helpful Hint: Write each function described in terms of the function f. For instance, if g(x) was half as large as f(x), then a(t)=1/2g(t). The values of function g are always three times as large as the corresponding values of function f.     The values of function h are always four more than the corresponding values of function f.

Q: Calculate the improper integral if it converges, or show that it diverges. 1 dx -

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Q: x*+2х+3

A: We can find the integration as below.  

Q: 2. Sketch the graph of f' given the graph of f. Explain how you found the answer. y 10- 9- 5- -10-9-...

A: The objective is to sketch the graph of f'.

Q: Let f(z) = z – 6z. Calculate the difference quotient (3+h)-{(3) - for h = .1 h = .01 h = -.01 h = -1...

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Q: proj„b is always less than |5 1|

A: We will use the definition of projection vector and will use the Cauchy-Schwarz inequality.

Q: A) What is the point of intersection between the plane x – 2 y +3 z +1 = 0 and the line r = + t? B)...

A: Use substitution method

Q: Evaluate the iterated integrals  ∫1 0  ∫1 0 dxdy

A: Given query is to find the value of the integral.

Q: b) Suppose that f(x) 1 if x is negative. Can ƒ be continuous at x = 0?

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Q: Differentiate y= 5x+5 dx

A: Given query is to find the derivative of the expression.

Q: Find an equation of the tangent line to y = 5 tan(x) at x =

A: Given problem:- Find an equation of the tangent line to y = 5tan(x) at x = π/4 .

Q: A particular country's exports of goods are increasing exponentially. The value of the exports, t ye...

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Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = e*Y sin(y)

A: The given function is: fx,y=exy siny To verify that the conclusion of Clairaut's theorem hold for th...

Q: The three series An, EBn, and ECn have terms 1 1 An 1 Cn = Bn n10 n Use the Limit Comparison Test to...

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Q: Show all of your work in this problem. Consider the infinite series k Σ k +1 k=1 (a) Write down the ...

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Q: A contour map of a function is shown. Use it to make a rough sketch of the graph of f. y A 14 13 12 ...

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Q: f(x,y), where x = x(r,s, t), Use a tree diagram to write out the Chain Rule for u y = y(r,s,t).

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Q: ii. cos(cos-G

A: Given query is to perform indicated trigonometric operation.

Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: Find all the values of x such that the given series would converge. In(n + 8) n= Answer: Note: Give ...

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Q: At what points is the following function continuous? 6x tan 3x y = x2 +2

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Q: What is the algebraic form of the complex number 13 e (A) 12+5i (в) 5-12i c) 12-5i D) 5+12i

A: We can find the exponential form of the algebraic expression as below.

Q: 1. Revenue is calculated by multiplying the price of an item by the quantity sold: Revenue = Price •...

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Q: 2. Let f(t) be a continuous function on the interval [0, 27]. Suppose the 1st order Fourier approxim...

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region a...

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Q: Write the equation of the sphere centered at (5, – 2, 4) with radius 3.

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Q: Find an equation of the plane that passes through P(4, 2, – 3) and is perpendicular to the line x+1 ...

A: Given that the plane is passes through the point (4,2,-3) and perpendicular to line x+1-3=y-12=z2

Q: I ... LL #3 The amount, A mg, of caffeine in the body t hours after drinking a cup of coffee can be ...

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Q: Express the surface area of revolution for: x = (y^4/4) + 1/(8y^2), 1 ≤ y ≤ 2; x@axis ( Express ds= ...

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Q: (х — 2)(х + 2)(г+ 1) (г + 3)(ӕ + 1)

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Q: Find the first partial derivatives of the function z = (2x + 3y)10.

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Q: Let S = E a, be an infinite series such that SN = 3 - n=1 10 16 (a) What are the values of E an and ...

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Q: Use a calculator to solve the following equation for 0 on the interval [–90°, 90°]. 3 sin (0) 4 Roun...

A: We can find the value in the interval as below.

Q: The following statement is TRUE except A. Derivative is the same as slope. B. A function is continuo...

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Q: Use y - x(x - 5)2 and its derivative dy - 5x(x - 3)(x - 5) to find each of the following. 18 dx 18 F...

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Q: 10. Show that the function f(x, y, z) = 2z³ – 3z(x² + y²) satisfies the Laplace Equation, = 0

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Q: A. ā xb = b x ā B. Jā + 5| = |a + b| C. It is possible for la + b| < [ā|

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Q: Determine the sum of the measures of the interior angles of the indicated polygon. Octagon The sum o...

A: topic- polygons and angles

Q: Given the triangle below, find the angle 0 in degrees. Round to the nearest degree. 17 9 Provide you...

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Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of...

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Q: Test the series for convergence or divergence. 3"n! 13 · 18 · 23 ... (5n + 8) n=1 Use the Select v a...

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Q: Test the series at the given values of x for convergence or divergence. (x+2)" Σ n=0 7" (3n + 1) • T...

A: Given the series is ∑n=0∞ (x+2)n7n (3n+1)

Q: Evaluate the lim lim

A: We will find the limits. 

Q: 6x+5x-1 lim X--1 7x-2

A: Topic = Limits

Q: Find the equation of the plane that contains the point (3, 2, 3) and the line  x = -4 +4t, y = -3t,...

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Q: The population of Hungary has been modeled by P = 9.919(0.998)',

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Q: 1. Find an equation of the line that is tangent to the graph of f and parallel to the given line. 1 ...

A: Topic = Functions

Q: x-7x3+101 g(x) = ズー1

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Q: Find the derivative of the function. y = a6 + cos6 x y'(x) =

A: Given

Q: Find the convergence set of the given power series: 2" x" n! n=1 The above series converges for < x ...

A: Given:   Limit equations is given

Q: -dx x´ +2x+3

A: The given integral,       ∫xx2+2x+3dx