Ceate five questions on the following topic along with the correct answers that you would expect if you were a teacher.   Functions (inverse of a function)

Q: Find the solution of the given initial value problem. cos t y%3D t 1 y' y(T) = 0, t >0 - t-1 y(t)

A: The given equation is; y'-y/t =cost/t-1; y(π)=0.

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

A: V(t) =1.6 e0.039ta)   substitute t=0 for 2006     V(0) =1.6e0= 1.6      Value of country's export in...

Q: Find the missing value for the radioactive isotope. (Round your answer to two decimal places.) Half-...

A: The given problem is solved below in detail.

Q: Use geometry (not Riemann sums) to compute the integral. dx 3 Enter a pumber

A: The given integral is  ∫12 x3dx

Q: 15. Solve the inequality. 7|x – 5| > 7 -4 < x < 6

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Q: Lim Ex +1

A: Here we have to evaluate limx→42x+1x-2

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: Management at a factory has found that the maximum number of units a worker can produce in a week is...

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Q: Let f (x) and g (x) be antiderivative of h (x), The which of the following is true? A None of the gi...

A: Application of derivative

Q: Draw a direction field for the given differential equation. Based on the direction field, determine ...

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Q: At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second poli...

A:

Q: Find and classify all critical points of the function f (x, y) = x* + y* - xy. 4(0) = 4 (010) D= 12(...

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect ...

Q: -x2 + 5x + 14 Evaluate lim x-2 -5x2- 2x + 16 Submit an exact answer.

A:

Q: What is the long term behavior of the solution with the initial condition (-2, 2)? 3 1 -1 5A4 -2 514...

A: Find your answer below 

Q: possible rational zeros given by the rational zeros theorem (but don't check to see which actually a...

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Q: Evaluate the integral f 2x (x² + 5) dx using the substitution 13 u = x +5. 2x (x² + 5)*° d =| +C

A: I =∫ 2 x (x2+5)13 dx  u = x2+5du = 2x dxI =∫ u13  du We know that,∫ xn  dx =xn+1n+1+C

Q: Evaluate the definite integral. 13 dx 3 (1 + 2x)2

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Q: S cos²(2x)dx

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Q: Suppose Gavriel's utility depends on the amount of time spent playing on Xbox (X) and the amount of ...

A:

Q: Evaluate the indefinite integral. 24 W cot(x) csc2(x) dx 24 cot?(x) + C 25 O (csc(x))24/25 + C 24 25...

A: To solve this use integration by substitution method

Q: 1. Determine whether the sequence converges or diverges. If it converges, find the limit. 52n + 5 (a...

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

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Q: Find the limit of the sequence using L'Hôpital's Rule. 1(Vn² + 11 – Cn = n - n (Use symbolic notatio...

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

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Q: Convert the point (1, , V3) from cylindrical to spherical coordinates. A. (2. 5. 5) 4' 6 В. 2,

A: To convert cylindrical coordinates (r, θ, z) to spherical coordinates ( ρ, θ, φ) we use following fo...

Q: Consider the function f(x) = 2/x + 4 on the interval 3, 10. Find the average or mean slope of the fu...

A: The function is given by fx = 2x+4 The interval is a, b = 3, 10 Mean Value Theorem: f'c = fb-fab-a =...

Q: 2. / 3" csc²(3") sin“(3") da (3") sin®(3") dx

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Q: 19. The polynomial f(x) = (x – 2)3 = (x – 2)(x – 2)(x – 2) has æ = 2 as a zero four times. True Fals...

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Q: 2. State whether lim f (x) and f(c) are equal or unequal at the given value of c. Also, state whethe...

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Q: he differential equation (8 – r²)dr = %3D r² (1n (;) – = 0 cos cos = 0 (r+ 4) (in (;) –

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Q: Ve dx

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Q: Find the limit of the sequence using L'Hôpital's Rule. (In(n))² an = 13n (Use symbolic notation and ...

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Q: Describe the surface of 4z2 – 4x² – y = 4 - |

A: The general equation of a  hyperboloid on two sheets is given by x2a2-y2b2-z2c2=1 notice that there ...

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

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Q: 13. What is the value of f(x) = 5 – 4lnx at x = 1? 3 9 5 undefined

A: NOTE: Refresh your page if you can't see any equations. .. here we have x=1

Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 – 7x)y² , y(0) : - ...

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Q: 43. The length {, width w, and height h of a box change with time. At a certain instant the dimensio...

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Q: Which of the following is the general solution to the differential equation y?dx = (xy – x²)dy? x In...

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Q: 1. Given f(x)= (a) Show that f'(x)= 2(x² -16) 3x by using the quotient rule. Hence, find all 11 the ...

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Q: ax +1) dx

A: we want to find the value of integral ∫ax2a(x2a+1)3xdx

Q: Determine the coefficient of Cot(x) when we evaluate J[cot(x) – csc(x)]²dx_ 1 A 2 1 В c) None of the...

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Q: Find the equation of the tangent line of y = 4e* at xo = 0. (Use symbolic notation and fractions whe...

A: y=4exSubstitute x=0y=4e0=4The point is (0,4)

Q: Find the inflection points of each of the given curve.  y = x3 – 3x2 + 4

A: ⊙a function y=f(x) is said to have inflection point at x=a, if its second derivative i.e. d2ydx2 cha...

Q: Find the derivative of the function. f(z) = e?/(z – 5) f'(z) =

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Q: T – 8r – 9 22. Evaluate 4 7² – 8x – 9 *xp: a. cosh -1X – 4 + C. sinh-1t – 4 +C b. 4 cosh -1x - 4 +C ...

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Q: Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west a...

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Q: 6x 4. У3 y = х+3

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Q: Find the angle, 0, that is cotermimal with 20T where 0 < 0 < 2T. Find the angle, 0, that is cotermim...

A: Coterminal Angles are angles  both have same initial side and terminal sides. To get coterminal angl...

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: 4. Figure 4.92 shows drug concentration curves for anhy- drous ampicillin for newborn babies and adu...

A: Basic calculus problem