Prove, using the definitions of tanh and sech in terms of the exponential function, that 1 − tanh2 (x) = sech2 (x).

Q: Find the absolute maximum and the absolute minimum for the function ƒ(x) = e¯ª – e¯5x " 0.598 ≤ x ≤…

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Q: Find the intervals on which the graph of f is concave​ upward, the intervals on which the graph of f…

A: f(x)=-x4+16x3-16x+5 If a function is concave up then f"(x)>0 If a function is concave down then…

Q: 1 cos³x -dx =

A: The given integral is 1/Cos3x.

Q: Show that 16x4+9y12 lim (x,y)→(0,0) 4x²+3y6 does not exist.

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Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: f(x, y) = x4 + 13x³y³ - 5xy4 + 14

A: Given: fx, y=x4+13x3y3-5xy4+14To Find: To determine ∂f∂x and ∂f∂y.

Q: J

A: Topic:- geometry      Definition :- system of equation is defined as  two or more equations that…

Q: 3. Algebraically rewrite the following equation using properties of logarithms and inverse…

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Q: 4. Identify the focus of A. (0,3) -(y - 3)² = (x-2). B. (4,3) C. (2,1) D. (2,5)

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Q: Find the area of the following region. The region inside the inner loop of the limaçon r = 2+4 cos 0…

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Q: nd f(7zº + 5x³) dx Find + C

A: Given:     ∫7x6+5x3dx=∫7x6dx+∫5x3dx=7∫x6dx+5∫x3dxwe know that ∫xndx=xn+1n+1

Q: Which of the following is an example of an inequality? 60 + |-3| = 63 60 + 2x < 120 60 - 2(15) =…

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Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

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Q: For f(x)=(sqrt x) + 2x , find the equation of the secant line passing through x1=4 and x2=9. Write…

A: Please see the below picture for detailed solution.

Q: dy dx = 2x2-5vxy = 4y2

A: 2x2-5xy=4y2We have to find the dydx

Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

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Q: A room in a certain factory wanted to improve the CO₂ concentration level which is a high 2500ppm.…

A: The air inside has 2500 ppm of CO2 and volume of 5000 cu.m  Fresh Air has 400 ppm of CO2    Now, let…

Q: dr 4+x² S Choices: tan ¹(x + 2) + C 1 In x² + 4 +C In x + 2+ C 1 tan 2 1 ¹ 1/2 + +C

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Q: ) Consider the function f(x) = 4x² - 8x on the interval [0, 6]. Find the absolute ex- trema for the…

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Q: An oil spill is pouring oil onto a sea in the shape of a circle. The slick is growing at a rate of…

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Q: 21. 22. 8) For problems 21 and 22, consider the graph of the function below. Determine the intervals…

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Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors x+8 x+8 x²+x-2…

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Q: The total cost of producing x newspapers is given by the function C(z) = 20x-x². Find the marginal…

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Q: Given f(x) = x² + 4 and g(x)=√x-2. Find (fog) (x) and write the domain of (fog) (x) in interval…

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Q: Consider the circle, x² - 8x + y² + 2y-8=0 i) ii) Write the equation of the circle in standard form.…

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Q: Suppose that the manufacturing cost of a particular item is approximated by M(x, y) = 6x³ x³y² +…

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Q: (b) Consider the complex vector space C² (with complex scalars). Find the real number a, if it…

A: The objective of the question is determine the value of "a" for which given vectors are linear…

Q: Jacob's father is planning to open a savings account to pay for Jacob's college education. He has…

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Q: The class outing ticket includes a snack-pack with three items, a cooldrink, chocolate and then…

A: Given tree diagram shows all the possible combination of "cooldrinks", "chocolates" and "chips or…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find each of the following when f(x) = t³d =…

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Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

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Q: For all x ER, it is known that 1. Find the value of f(2022) (0). +∞o 2. Find the exact value of f(x)…

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Q: it is planned to construct a right circular cylindrical steam boiler. the available budget for the…

A: Given data:- The available budget for the cylindrical steam boiler, =1 million=1000000 The cost of…

Q: Find +62+7) dr 1(2²³/20 +C

A: Integration  ∫3x2+6x+7dx

Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors

A: Given So we do partial fraction to get Distinct linear factor and Repeated liner factor

Q: [2 2x log 2x dx

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Q: 4. Verify if the following equations general solution: are exact and find the 2 9. 2xydx + (1 + x²)…

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Q: Solve the system of equations eie= cose -isin (0) in(e) is the imaginary unit and is the base of the…

A: Given system of equations eiθ=cosθ+isinθe-iθ=cosθ-isinθ

Q: Use the graph of y=f(z) for problems 7 and 8. Use the plot above to determine lim f(x) and lim f(x).…

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Q: T/F: The half-life of the exponential function P(t) = et is T = ln(2).

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Q: What are the factors of x2 + 7x - 30? (x + 6)(x - 5) (x + 10)(x - 3) (x - 10)(x + 3) (x - 6)(x+…

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Q: For each positive integer n, define an = n² sin +∞ 1. Determine if the sequence {an} converges or…

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Q: Two fire-lookout stations are 14 miles apart, with station B directly east of stat notation is N35°F…

A: Let the position of fire be at C. Given, Distance between two fire lookout stations AB= 14 miles…

Q: If evaluate f f(x) dx = 7 f(x) dx = 8 f2f (x) dr.

A: Topic = Integration

Q: question

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Q: . For each positive integer n, define an = n² sin +∞ 1. Determine if the sequence {an} converges or…

A: The solution is given below

Q: Explain how you would decide between using the substitution method or the integration by parts…

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Q: CALCULATE THE AREA BETWEEN THE GIVEN FUNCTIONS. DEVELOP THE PROBLEM WITH ALL STEP EXPLAINED AND…

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Q: Divide: 2ху x2y+3xy %. 4x+12 x2+6x+9

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Q: Q/ Evaluate the following integrals. S f sec40 tan²0 de

A: W have to find the integral.