dy dx y = u54 and u = 3x² - 2x² dy du du' dx Find and

Q: Find f'(t) if f(t)=4t² +8t+3.

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Q: an = 2n + 5 245) 4n+1

A: First, let's consider the limit of the sequence as n approaches…

Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

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Q: Find an equation of the tangent line to the curve at each given point. x=2-3 cos 6, y = 3 + 2 sin 8…

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

A: To determine the given equation is linear or non linear.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Consider the sequence

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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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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Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x+y=5,…

A: Equation of plane : and equation of cylinder : Find the volume of the region in the first octant…

Q: +² dt F(x) In(t) F(x), determine whether F is inc a dec x>2 at x=2020

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Q: Consider the following parametric curve. Find dy dx dy dx dy dx = Find the value of X = sin (6t) +…

A: Equation of the line : (y-y1) .

Q: Find the lines that are tangent to the curve y = 2tan(pi*x/4) at x=1

A: The equation of tangent line passes through point  with slope

Q: (b) Use the Fundamental x² :) = ( 4 – t) 1 F(x) = S(4 Chly appr Theorem of Calculus to calculate…

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Q: (2) Solve the given homogeneous equation by the appropriate substitution y dx (x + y) dy = 0. - You…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x²² In(x),…

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Q: A 13 ft ladder is leaning against a house when its base starts to slide away. By the time the base…

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Q: Two sets A and B are defined as follows: A = {x, y, z); B = {1, 2, 3}. Ug Oh f range of g range of h…

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Q: cb+2π f" sin z dz = Sov20 a+2π a sin x dx

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Q: Consider the following. 8n 77 Calculate, to four decimal places, the first ten terms of the sequence…

A: The sequence is given by :-

Q: Find the absolute extrema (max and min) of f(x,y)=3x^2-2y^2 over the disc x^2+y^2<=1. Indicate all…

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Q: Suppose that in a certain biology lab experiment, the number of bacteria is related to the…

A: Suppose that in a certain biology lab experiment, the number of bacteria is related to the…

Q: Consider the following. Find y'(x). y'(x) = y = X = X x² +9 Find the critical numbers of y(x).…

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Q: A rectangular beam is cut from a cylindrical log of radius 50 cm. A cross-section of the log is…

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Q: 2. Determine whether the series n Σ» (-1) (3) converges or diverges. If it converges, find the sum.

A: The given series is

Q: (a) Find and sketch the domain of the function f(x,y)=√x-1+√y-4

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Q: Complete the table to find the derivative of the function without using the Quotient Rule. Simplify…

A: Rewriting expression

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: Solve the second order. 1. eq Y Ý + Y

A: The given differential equation is

Q: Consider the function INTERMEDIATE WORK Using calculus give a sketch of y. Make sure you include the…

A: The given function equation is

Q: The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of…

A: Please solve the given problem using the concept of derivatives.

Q: Given that (fog)(x)=x-8, which are correct rules for f(x) and g(x) that result in this composite…

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Q: Find a Cartesian equation for the curve. r = 9 cos(0)

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Q: The line given by the parametric equations x= 3+2t, y=4-t, z=1 + 3t passes through the point (11, 8,…

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Q: Let f(x) = -x+7 and g(x) = x^2 -2 evaluate the expression f(g(1))

A: We have to find f(g(1)) for the given function. It is a example of composite function. We replace x…

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The equation of the curve is given byTo determine: The slope of the tangent line to the given curve…

Q: Solve the given initial-value problem. y(x) = 2y" + 3y - 2y = 10x² - 4x 13, y(0) = 0, y'(0) = 0 -

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Solve the following initial-value problem: dy dx = e sin x 2xy e cos x + x² y(0)=0

A: Given differential equation

Q: Use spherical coordinates. Evaluate xex + y2 t2 + dV, where E is the portion of the unit ball x² +…

A: To find  E is the portion of the unit ball  that lies in the first octant

Q: Describe the x-values at which the function is differentiable. x² y = x² - 49

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Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. tan(5x…

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Q: Evaluate the following integral using integration by parts. Se 10x cos x dx

A: I=∫e10xcos⁡xdx

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: r=6cos⁡(θ),θ=π3

Q: Differentiate the given function. 8 (71 + 1/ ) (71²-9) F(t)= 7t =

A: we need to differentiate the given function.

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: Sx ³√x²+4 3 S

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Q: Roberto has plans to build a tree house in his backyard. He takes measurements from the ground and…

A: Here,

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

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Q: Solve the equation for x in terms of the other letters. (Enter your answers as a comma-separated…

A: Given data

Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: The function is given byTo determine: The value of the second derivative of the function at point

Q: Find the lines that are tangent to the curve y=2tan(pi*x/2) at x=1

A: The equation of tangent line passes through point  with slope