Given that f(x) = 4x+1 and h(x) = x°, find (h o f)(2).

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the oute...

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Q: Consider the following graph. y 12 (13,11) 8 (1,2) (13,2) X 4 8 12 (a) Find the length of each side ...

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Q: ydx+(2x+3y)dy=0 solve by using homogeneous equaations

A: We know,∫dxx=ln(x)   Given differential equation, ydx+(2x+3y)dy=0 ⇒dydx=-y2x+3y....(i)  

Q: Evaluate the definite integral. 1 e? + 6 dz Jo ez + 6z

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Q: Use the difference an+1 – An to show that the sequence {n – 7"t00 is strictly increasing or strictly...

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Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt dy dt 15, find dy/dt when x = 4...

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Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to t...

A: Since u denotes the temperature of an object, dudt ∝ (u - ua)dudt = - k (u - ua)(Negative sign impli...

Q: Find the slope of the line tangent to the graph of f(x) = 3x² - x- 5 at x = 1.

A: The equation of the curve is given by fx = 3x2-x-5 The point is x = 1 Formula Used: mtan = dfdxx=1 T...

Q: 1 dx x/1+ x6

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Q: A fuel tank is being designed to contain 200 m3 of gasoline, but the maximum length of a tank (measu...

A: We have to find the height and radius of the fuel tank which costs minimum using differentiation.

Q: A chemical substance has a decay rate of 8.3% per day. The rate of change of an amount N of the chem...

A: The solution can be seen below.

Q: Direction: solve and analyze each of the following problem in neat and orderly manner. Do this in yo...

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Q: Use the appropriate limit laws and theorems to determine the limit of the sequence. (1+9) 6. an = %3...

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Q: Given that lim f(x) = 0 lim g(x) = 0 lim h(x) = 1 %3D %3! Xa Xa lim p(x) = 0 lim q(x) = 0, %3D Xa Xa...

A: We have to solve the limits.

Q: Given a particle is moving in a curve r(t) = cos 7t i + sin 7t j + 6t k. Find the tangential compo...

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Q: Find the slope-intercept form of the equation of the tangent line to the curve defined by x-2 3 fra)...

A: Equation of tangent line at the point (a,b) of the curve y=f(x) is f(x)-f(a)=f'(a)x-a

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation an...

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Q: For the next five questions, consider the following differential equation: (7 + zy')dr + (5y – ry + ...

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Q: x2 – x +1 When you evaluate: dx. The sum of the coefficient of X" for any constant n>0 js 26 15 23 B...

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Q: Total profit is defined as total revenue, R(x), minus total cost, C(x), and is given by the function...

A: First we find out P(x) using P(x)=R(x)-C(x)

Q: Answer the following True or False: Two cars drive from one spotlight to the next, leaving at the sa...

A: We can state the answer true or false with reason as below.

Q: Suppose y = V2x + 1, where x and y are functions of t. (a) If dx/dt = 15, find dy/dt when x = 4. dy ...

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Q: Items 15 The graph of a function f is shown. On top of the graph of f, sketch the graph of f'. Use a...

A: The graph of the functions are given as 

Q: Given that lim f(x) = 0 lim g(x) = 0 lim h(x) = 1 %3D Xa Xa Xa lim p(x) = 0 lim q(x) = 0, %3D Xa Xa ...

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Q: If a series converges, then either it converges absolutely or it converges conditionally.

A: Given:        Absolute convergence:          A series ∑an converges absolutely if ∑an converges.    ...

Q: 1. Find the following limit, if it exists. lim (z.1)-(0.0) V2 + y? +1-1

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Q: Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by...

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Q: V3 2 dy 1- у?

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Q: Let A, B and C be any sets. Which of the following is equal to (A U C) n (B \ C)? Select one: a. (A ...

A: Solution is given below:

Q: A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactiv...

A: Given query is to find the amount of the substance after 29 hours.

Q: Solve. 3r = 27r The solution(s) is/are. (Simplify your answer. Use a comma to separate answers as ne...

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

Q: The curve y = f(x) has a y – intercept of 3. The tangent to this curve at the point (x, y) has an x ...

A: Based on x and y intercept value we will find out equation of the graph. 

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

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Q: Express the repeating decimal as a fraction. 0.1111. . .

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Q: In 2004, an art collector paid $60,791,000 for a particular painting. The same painting sold for $30...

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Q: c 2 0 0 4 0 1 0 40

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Q: Find the area of a triangle bounded by lines y=2x and x=1 by a.) single integration b.) double int...

A: Given: - The lines are, y=2x and x=1  To find: - The area of a triangle bounded by given lines. (a) ...

Q: Find the inflection points of each of the given curve.  y = 5x – x5

A: Given :y=5x-x5

Q: Compute the directional derivative of the following function at the given point P in the direction o...

A: We have to find the directional derivative of the function f(x,y).

Q: Use the appropriate limit laws and theorems to determine the limit of the sequence. in an = sin (Use...

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Q: Differentiate. sin(0) f(0) 1 + cos(0) f'(0) =

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Q: Find torsion of the motion r(t) = . Leave your answer correct to two decimal places.

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Q: EVALUATE INTERMS OF GAMMA FUNCTION.

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Q: If we apply Rolle's Theorem to the function f(r) -2r 16r 8 on the interval 2, 6, how many values of ...

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Q: A. Each week, Adriel buys cheese (C) and sausage (S) which provides him a utility of U= 6th root of ...

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Q: 9. The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the y-axis....

A: The graph of a quadratic function is always a parabola.

Q: f(x) =In(tan¯'x)

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Q: 8. -8-7 1 Select the correct answer below: O f(x) has a removable discontinuity at x = 6. O f(x) has...

A: From the given graph we can see that at x=6 the curve has a dot ( but not a hole). 

Q: For vectors ū = (1,-5,2) and v = (3, 1,-4), calculate the following: a) ū• i b) the angle between ū ...

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Q: 11. Solve the equation logs (3x + 9) = log5(5x – 3)?

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