A. Logarithmic and Exponential Functions 1. y = log 2. t= In tan (; +) 3. y = In (e²x²)

Q: Evaluate the indefinite integral. S(4v – v²)² dv , and Show the complete solution and express the fi...

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Q: t. 1. lim 0 sin t 2. lim 10 et-1 sin(2t) 3. lim t-+0 2t

A: Use simple limit formula or L hospital rule.

Q: 8. O f(x) = 3x° – 5x³ + 1

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Q: 2n (a) ) n + 2 n=1

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Q: Let y= (x+sin(x))^5 Find g(x) and f(x) so that y= (f∘g)(x), and compute the derivative using the Cha...

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Q: Find the average value of the function f(x) = 3x2 on the interval 2 <x < 6

A: Given,            The function is fx=3x2 and the interval is 2≤x≤6.To find : The average value of th...

Q: f(t) = – 29 cos (t) + 78 %3D Find the average temperature from month 2 to month 6

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Q: Use the following graph and write the shaded area as integrals. A(-1,3) D(2,1) B(0,0) y = h(x) y = f...

A: To write the shaded area as an integral. Given information: The graph is shown below.  

Q: The frequency F of a fire truck siren heard by a stationary observer is given below, where i v repre...

A: For the solution follow the next steps.

Q: Find the equation of the Line tangent of xy-y^3 =-6 at the point (2,2) Find the equation of the lin...

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Q: The first derivative of a continuous function y = f(x) is given. Find y'" and then sketch the genera...

A: topic -  derivative and graph

Q: From 2000 to 2007, the mean household income in the United States rose by an average of approximatel...

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Q: A producer of perishable product offers a wage incentive to drivers of its trucks. A standard delive...

A: We have to find the maximum time and maximum salary for the driver.

Q: Consider the function F(x) = X-3sinx Find the indicoled limit 2'Hôpitel's Rulei slete thet it does n...

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Q: Find all the zeros. Write the answer in exact form. m (4) = 5x -x- 35x+7 If there is more than one a...

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Q: Use the limit comparison test to determine whether the series converges or diverges. 8k2 – 6k + 6 16...

A: On solving this we will get

Q: The angle of depression from a window to a rock to the ground is 67.8 degrees. What is the angle of ...

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Q: Suppose the infinite series an is divergent. Then for any constant c, the series n=1 can is also div...

A: This is a problem related to series and sum calculator. Based on the available concept we will prove...

Q: Evaluate the indefinite integral. (x2 – 6x + 9)dx , and • Identify what is the u=? and du=? Show the...

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Q: A one-to-one function is given. Write an equation for the inverse function. X-4 v (x) = x+5 (x) = D

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Q: Consider the indefinite integral *7x³ + 9x² + 12x + 24 -dx x4 + 4x2

A: Given,            ∫7x3+9x2+12x+24x4+4x2To find : The partial fractions decomposition.

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use ...

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Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola - 15.32y = 2...

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Q: Fin the equation of the line tangent F(x) = xcos(x) + e^x at the point (0,2)

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Q: Your are driving away from Toledo. Your distance (in miles) away from Toledo x hours after 12:00 noo...

A: We will find the maximum distance north of your home that you reach during the trip as following.   ...

Q: A particle moves along the curve y = V1+ x3. As it reaches the point (2, 3), the y-coordinate is inc...

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Q: The following function is a company's price function, where p is the price (in dollars) at which qua...

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Q: A cylindrical tank with radius 5 m is being filled with water at a rate of 4 m³/min. How fast is the...

A: Find your answer below 

Q: Let F(x) = f(x*) and G(x) = (f(x)) . You also know that a' = 13, f(a) = 2, f' (a) = 5, f'(a³) = Cind...

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Q: 00 6. nニ)

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Q: A spherical balloon is inflated so that its radius (r) increases at a rate of 1/3cm/sec. How fast is...

A: Vloume(V)=43πr3Differentiate w.r.t tdVdt=43π.3r2.drdt

Q: Calculate the derivative of y with respect to x, if x^4y+4xy^4 =x+y. dy/dx =

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Q: 1. Find the truncuated error of the Maclaurin series sinx cosx given that is truncated into 3 terms....

A: This is a problem of series expansion. Maclaurin series is nothing but taylor series expansion at va...

Q: How many fraction terms are there in the partial fraction decomposition of x3 + x2 + 5 ? æ(2x – 5) (...

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Q: Find the number(s) b such that the average value of f(x) = 6x² – 62x + 132 - on the interval 0, 6 is...

A: Given   fx=6x2-62x+132   ,    favg=15      We have to find b value for interval [0,b]

Q: Problem 6. Consider the curve defined by y2 – 4xy + 2x? = 7y. Write the equation of the tangent line...

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Q: 6. Let a be a real number. Consider the series where an = cos(n7); 2n + 1 n=0 (a) Is it possible to ...

A: Given: α∈ℝ,  the series ∑n=0∞ an;  an=cos(nπ) αn2n+1

Q: x-2 6) Find the antiderivative: - (x+1)2+4

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Q: The weekly cost C, in dollars, for a manufacturer to produce q automobile tires is given by C = 2300...

A: Answer: The solution is as given below:

Q: Determine whether the two functions are inverses. -4 4x-4 t (x) = and v (x) = x-4 The two functions ...

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Q: Simplify the expression without using a calculator. log

A: log√61 = ? Here we use property  logab = logkb/(logka) Use this  log101/(log10√6) log101 = 0 So the ...

Q: sequence is defined recursively as sk = sk-1 + 3k  for k ≥ 2. s1 = 4 s2 =  s3 =  s4 =  s5 =

A: A sequence is defined recursively as sk = sk-1 + 3k  for k ≥ 2. s1 = 4

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -...

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Q: Find the vertex, focus, and directrix for the parabola (x + 1)² = 8(y + 2) Vertex: Focus: Eguation o...

A: Topic = Parabola Vertex  (-1,-2) Focus ( -1,0) Equation of the Directrix , y= -4

Q: Find an equation of the parabola that has a focus at (2, 17) and a vertex at (2, 9) y = Find an equa...

A: Follow the procedure given below.

Q: JA- IF f(x) = |Vx- 4, g) x, Find fog(x) Then graph it & determine (domain ,rang Vi- 2cotx B- Granh t...

A: Find your answer below 

Q: Q2) Find : (a) lim (2 + x) x-4+ 16-x 1-secx 0 sinx cos2x sintx (b) lim (c) lim (d) lim x-0 sin2x cos...

A: Dear student, According to bartleby guidelines when student post more than one question then expert ...

Q: Find the value of k that will make the function f(x) continuous. -x2+8, if x+ 3 f (x) =, k, if x=3

A: topic - limits and continuity

Q: B. Find the sor and aguation of the TANGENT and NORMAL LINE to the curve Graph cach curve, normal, a...

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Q: Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. As...

A: Topic = Algebra