Find f'(t) if f(t)=4t² +8t+3.

Q: Sx ³√x²+4 3 S

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Q: To test this series for convergence ∞ n=1 n n6 + 7 You could use the Limit Comparison Test,…

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Q: If f(x) = f'(x) = f'(4) = tan x - 5 sec x 3x² tan(x) sec(x) X

A: The Quotient Rule:Use the common derivatives:

Q: √3 4 16 (x-7)(x + 9) dx

A: I=∫3416(x−7)(x+9)dx

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A: Given the table below gives the velocity of a runner at half-second intervals during the first three…

Q: If f(x) x = [²₁ 1 = = then ƒ'(x) = ƒ'(−2) = tadt

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Q: The equation r³+ y³ = 3ry defines a curve named as the Folium of Descartes. (a) Use implicit…

A: The equation  defines a curve named as the Folium of Descartes.By using implicit differentiation to…

Q: Consider the following. f(x) = √√49 - x² Find the critical numbers. (Enter your answers as a…

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Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6, 1) y…

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Q: The number of books checked out from the library from 25 students are as follows: 0; 0; 0; 2; 2; 3;…

A: Consider the data 0,0,0,2,2,3,3,4,4,5,5,6,7,7,8,8,8,8,10,10,11,11,12,12

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. 11.…

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Q: Find a Cartesian equation for the curve. r = 5 sec (0) 2π X

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Q: Give the partial fraction decomposition for the following function. 2 x²-2x-8 2 2 x-2x-8 ||

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Q: The indicated function y₁(x) is a solution of the associated homogeneous equation. Use the method of…

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Q: 2 xy dy + 4y dx = 8 x dx 2 2

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Q: (a) Consider the curve y = x - 3x7. d.x (b) This function is not differentiable when = (c) (Give…

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Q: Solve the equation. 7 X-4 X = 5 2x²5x- 12 X 1 2x + 3

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Q: Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros: 1;…

A: Form a polynomial f(x) with real coefficients having the given degree and zeros.Degree 5 ; zeros: 1…

Q: a 5. At 2:00 PM jogging at 8.5 mph. starts from the same place, heading East at 60 mph. the driver…

A: At 2:00 PM a runner heads east on a highway, jogging at 8.5 mph. At 3:00 PM, a driver starts from…

Q: Find the derivative b. y= sec^-1(2x+1) c. y=x^e^x

A: I have appended the formula used in the solution procedure.

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Suppose that lim ƒ(x) = 0, lim g(x) = 0, lim h(x) = 1, limp(x) = ∞, and x→a x→a x→a x→a lim q(x) =…

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Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

A: To state the order of the given ordinary differential equation. To determine whether the equation is…

Q: Sketch the level curves of the function corresponding to each value of z. f(x, y) = 4x + 6y; z = -2,…

A: Consider the function

Q: Use the alternative form of the derivative to find the derivative of the function f(x) = x³ + 8x, X…

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Q: 9. If f(x)=x²-2x+7, evaluate each of the following

A: The given function is To find:-

Q: 2) Draw a direction field for the given differential equation. Based on the direction field,…

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Q: Suppose f(x, y) = x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: For which values of x are the vectors (2x, 4, x) and (-1, -2, x) orthogonal? Select one: O None of…

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Q: Consider the following. f(x) = x² + 16 Find the critical numbers. (Enter your answers as a…

A: The function f is increasing on I if f'(x)>0 for all x in I.The function f is decreasing on I if…

Q: Consider the following differential equation to be solved by the method of undetermined…

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Q: The graph of y = f(x) is given below. -5 150 num -4 lim f(x) AI-1 -3 -2 5 4 3 2 -1 -1/ 1 2 4…

A: A graph of the function  is given.The aim is to find the given limits.

Q: Find the volume of the region between the cylinder z = 2y² and the xy-plane that is bounded by the…

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. 5 r…

A: r=5θ,π2≤θ≤2π

Q: Find the absolute maximum and absolute minimum of the following function on the given interval. 1…

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Q: 1. Find the derivative of: a. y=(x-1/x+1)^2

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: What is the unit tangent vector T(t) on the curve r(t) = (sin(t), 3, 2 cos (2t)) when t = 0? Select…

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Q: 3. Consider the circle as a vector-valued function r(t) = cos(t)i + sin(t)j. Calculate limt→+∞ r(t)…

A: Find the limit

Q: The given curve is rotated about the x-axis. Set up, but do not evaluate, an integral for the area…

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Q: dy d²y Find and dx dx² x = t² + 2, y = t² + 3t dy dx d²y dx² For which values of t is the curve…

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Q: 5 4 --3- 2 -1

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Q: 6. Let f(x, y) = sin(x + y). Answer the following questions. (a) ) Find the gradient f(x, y). (b)…

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Q: Use partial fraction decomposition to find the following integral -da 24-1

A: I=∫x2x4−1dx

Q: For which value of t does the line given by the parametric equations x = t -1, y = 1+ 2t, z = 3 - t…

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Q: A window has the shape of a parabola above and a circular arc below. Find the area of the window.…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: To find the critical numbers of the following function.

Q: 3. Given that w = xyz + y² + x + 1, x = et, y = 82, 2=t+1. ) Find Ow/as. (b) (c) Find 0w/Ot. Find…

A: Given that .(a) To find .(b) To find .(c) To find .Note: Since the student has posted many sub-parts…

Q: Tel f(x) = at: *+] at x = 2

A: The given function is

Q: Use the quotient rule to find the derivative of -10 sin(x) - 1 6x² +5 You do not need to simplify…

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