Differentiate the function. f(x) = sin(5 In(x))

Q: Find f'(a). f'(a) = F(E) 6t+ 6 t + 3

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Q: Find dy dx dy dx for y = √u and u = x2 + 3.

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Q: 8. Consider the implicity defined relation 3 sin x + cos y = xy for 0 < x < 2л. What are the…

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Q: Does the series 1 √√nº +4 n=1 O converges O diverges converge or diverge?

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Q: Find the limit. (If the limit is infinite, enter 'co' or '-00', as appropriate. lim v 3

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Q: y = x³, y = 0, X = 1, X = 4

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Q: Find y as a function of a if y (0) = 2, y'(0) = 9, y'(0) = 4. y" - 5y" +6y= 0,

A: y′′′−5y′′+6y′=0,y(0)=2,y′(0)=9,y′′(0)=4

Q: Which of the following are continuous functions? (Select all that apply.) The temperature at a…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: EXAMPLE 5 Video Example Where is the function f(x)=(x) differentiable? SOLUTION If x > 0, then [x]-…

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Q: 10. The graph of y = 4 |x|-7 is symmetric with respect to which of the following? A. y-axis C. y = x…

A: (i) x-axis symmetry- if we put y=-y and we get the original equation. than the function is symmetric…

Q: (1) dz log (in z) 4².

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Q: The implied domain is the set of all real numbers for which the expression is defined. The domain…

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Q: Consider the following functions. f(x)=x-8, g(x) = x² Find (f+g)(x). (f+g)(x) = Find the domain of…

A: The given functions are  and

Q: (a) Suppose the number of mosquitos in a room can be modeled over time by m(t) = 14 sin(t/12) + 92.…

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Q: When writing the solutions for limit problems (and problems in general), we want to communicate our…

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Q: What value(s) of & are an appropriate choice when proving the following limit?

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Q: Use the alternating series test to determine whether the series n² √n¹ + 17 Σ (-1)+1. n=1 converges…

A: The given series Alternating series TestSuppose that we have a series  and either 1) 2)  is a…

Q: How long will it take $2,000 to grow to $8,000 if it is invested at 6% compounded monthly?

A: The compound interest formula to find the amount after t years is here r is the interest rate.p is…

Q: Explain the difference between average and instantaneous rates of change. As part of the…

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Q: Problems 9-18, The graph of a polynomial function y = f(x), is shown at right. Identify the…

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Q: 6. Find the lim (x²-3)³ (x³ + 2)²x

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Q: Find the derivative of the function using the definition of derivative. g(x)=√6- State the domain of…

A: g(x)=6−x

Q: The table shows the position of a cyclist. t (seconds) s (meters) (a) Find the average velocity for…

A: The position of the cyclist is given as below,We have to find the instantaneous velocity at t=3…

Q: Differentiate the function. y = ex +4+3 y' = et+4+3 X

A: The Sum/Difference Rule:The Power Rule:The Chain Rule:And use the common deriavtive:

Q: 2. Sketch the graph of this function: g(x) = 0, if a ≤ 0 x, if 0 < x < 100 100 0, if x

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Q: 4. Calculate the followings for the given vectors = 2i-j- 2k, v=2i3j+ k, w = i + j-k; a) The vector…

A: In this question, we will find the projection and volume of the tetrahedron.

Q: Using the given graph, approximate the area under the curve from x = 3 to x = 6 using 3 subdivisions…

A: Find the area of the given graph using left endpoint

Q: Differentiate the function. h(t) = √t - Bet Vt h'(t)= =

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Q: 2. Use the graph of p(n) below to answer the fo (pin) 2 0 -2 (a) What is p(1)? (b) What is p(0)? (c)…

A: The graph of  is given below.(d) To solve .(e) To find the values of  if (f) To solve .

Q: Prove that if f(x) and g(x) are continuous at a and c is a constant, then the function cf(x) + g(x)…

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Q: 3. Use Desmos to graph the function f(x) = 4x³ + 10x² - 1 and answer the following questions. (a)…

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Q: (4) A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells z…

A: A soft-drink vendor at a popular beach analyzes his sales records, and finds that if sells x cans of…

Q: sgn(x) = O -1 0 1 ketch the graph of this function. y (1) if x 0 2 lim sgn(x) 2 4 X (b) Find each…

A: sgn⁡(x)={−1 if x&lt;00 if x=01 if x&gt;0

Q: U in the interval (0.5, 1). Part b) Use your graphing calculator to find an interval of length 0.01…

A: f(x)=ln(x+1)-x3

Q: 2. Let p(x) = -3x + 12. (a) Graph p(x) on the domain -3 ≤ x ≤ 5. Label the intercepts. (b) Solve…

A: p(x)=-3x+12

Q: Find the derivative of the function. x x+5

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Q: A bank features a savings account that has an annual percentage rate of r = 3.2% with interest…

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Q: How can I find the area of the region bounded by the given curves for y2 = x, y3 = x. The answer…

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Q: Which of the statements describe continuous functions? Select all that apply. The cost of an airline…

A: We have to select the correct answer for the continuous function

Q: Find the lim (√9x² + x - 3x)

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Q: Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line…

A: Given that a line passes through point  and parallel to line

Q: Evaluate the following limits. If needed, enter oo for oo and -oo for co, and DNE if the limit does…

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Q: Find parametric equations for the line through the point (0, 3, 2) that is parallel to the plane x +…

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Q: Find all numbers b such that the average value of f(x) = 3 + 10x - 6x² on the interval [0, b] is…

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Q: Differentiate the function with respect to y. 11 Bey 10

A: Given the function The aim is to find the derivative  with respect to .

Q: derivative of in, in (-3,0) the direction of P P(-3,0),

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Q: Solve the problem. The total cost in dollars for a certain company to produce x empty jars to be…

A: C(x)=0.6x+23,000

Q: We want to use the Alternating Series Test to determine if the series: ∞ Σ(-1) ²k+1_ k=1 k² k6 + 19…

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Q: (2) Let f(x) = -3 sin (1x + 1). (d) State how you can obtain the graph of y = f(x) based on the…

A: Given the function y=sin(x).

Q: The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and…

A: The temperature in degrees Celsius on the surface of a metal plate is given by T(x,y), where x and y…