If f(x) -6₁² = 2 f'(x) =| t³ dt then

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Q: 2 2 Find the area of the region between the curves y = 4x² - 4 and y=-3x +3 from x= -1 to x= 1.

A: The required area is the shaded region in the graph

Q: Find the Taylor Series for f(x)=x²³+x²+x+1 about a=1

A: The given function is The Taylor series for f(x) about

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A: Given that a patient has an illness that typically lasts about 24 hours. The temperature, T, in…

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Q: TU Find the speed for c(t) = (3 sin(5t), 8 cos(5t)) at time t = FR

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A: The objective of this question is to find the intervals on which the graph of the function f(x) = -x…

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Q: Find a, b, c, and d such that the curve y=ax^3+bx^2+cx+d has its tangent line at (1, 1) and at (0,…

A: To find such that the curve  has its tangent line at(1, 1) and at (0, -2) are parallel to lines…

Q: Evaluate the expression without using a calculator. log 8√√512

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Q: 5. Find two antiderivatives of f(x) = x0.8 - 3e²¹ + π cos(2x)

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Q: Determine the value of the following definite integral. St dz 15x+20x³ 3x²+2 Leave your answer in…

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Q: Evaluate each expression using the graphs of y = f(x) and y = g(x) shown below. a) (gof)(2) b)…

A: To evaluate each of the following expression by using the graphs of  shown below.

Q: The temperature of a town t months after January can be estimated by the function…

A: The temperature of a town is defined by .The aim is to find the average temperature from month  to…

Q: Use l'Hôpital's rule to find the limit. Use -∞o or ∞o when appropriate. 3x²+5 lim x→∞04x³ +2 Select…

A: The objective of this question is to find the limit of the expression (3x²+5)/(4x³ +2) as x…

Q: Suppose we are trying to show that lim f(x) = L where the graph of f (x) is given below. A distance…

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Q: K Find the indefinite integral √(-2 -2 sec x tan x +5 sec x +5 sec² x) dx = -2 sec x tan x +5 x) dx.

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Q: Select the graph for which f(x) > 0 and a) r f(x) < 0

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Q: Find the center and the radius of the sphere. +z-3x+6z=0 x +y +z

A: The given equation of sphere is:To find the center and the radius of the sphere.

Q: Given the graph of f(x) below. Determine the average rate of change of f(x) from x = -2 to x = 2.…

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Q: Obtain the following limits: lim (1+ x48 1 lim x-0 3x X 1 sin 3x

A: L=limx→∞(1+1x)x

Q: Use a Riemann sum to approximate the area under the graph of f(x)=x on the interval 3≤x≤5 using n =…

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Q: Solve the initial value problem below using the method of Laplace transforms. ty'' - ty' + y = 5,…

A: The initial value problem is given as,solve the problem.

Q: Write the following expression in expanded form. +5 log X+7

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Q: Evaluate the surface integral      SF · dS  for the given vector field F and the oriented surface…

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Q: 256x The volume of a sphere is increasing at a rate of 3 cm³/sec. Find the rate of change of its…

A: The expression for the surface area of the sphere is:Where r is the radius of the sphere.The…

Q: At time t, the position of a body moving along the s-axis is s=13-1512+72t m. Find the body's…

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Q: -10 -8 -6 -4 -2. 9 55 40 -6 16 V 4 O 8 10 TERMATH Write the standard equation for the hyperbola…

A: given graph of hyperbola

Q: Match the graph of the function on the left with the derivative on the r 1. a. 2. 3. 4. -10 10 -10…

A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…

Q: A landscape architect would like to design a rectangular flower garden with an area of 128 square…

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: The length of the polar curve r = f(θ), θ varies from a to b is given byL = ∫a b √((f(θ))2 + (…

Q: them by mteger values. For each of the following logarithmic expressions, give the two integers that…

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Q: Use complex number operations to determine the solution to the expression below. The final solution…

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Q: Suppose that functions f and g and their derivatives with respect to x have the values shown to the…

A: As per the company's guidelines, we are supposed to solve the first three sub-parts for you, Kindly…

Q: (4) Find the maximum and minimum values of f(x, y) = xy on the ellipse x² - xy + y² = 1.

A: The given equation of function  Let

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Q: for Integrals Find or approximate all points a which the given function equals its average value on…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Find an antiderivative of the function g(t) = e-³t. An antiderivative is

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Q: The position of a particle moving along a coordinate line is s=√52+4t, with s in meters and t in…

A: The position of a particle moving along a coordinate line is s=52+4t, with s in meters and t in…

Q: Problem #8: Use Divergence theorem to find the outward flux of = (3x², e¹², cos³ (1² + x)) of the…

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Q: Evaluate the following integral. 2 | (0²-0 -2 (4y -6y+6) dy

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Q: Find the value of (fog)' at the given value of x. Assume that f'(3)=8, g'(4) = -6, g(4)=3, and y =…

A: The chain rule of differentiation is given by

Q: 7. Consider f(x) = for X for (x-3)² for (a) Sketch the graph of f. 3-x (b) Find each limit. (i) lim…

A: as per our guidelines we can answer only 3 sub parts of a given question so kindly repost the…

Q: Find an antiderivative of the function h(y) = 3y² — y6. An antiderivative is

A: .

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Q: Prove that the equation is an identity. (sin 0 - cos 0)² + 2 cos 0 sin 0 = 1 Working from the…

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Q: The equation of a hyperbola is (y + 3)2 - 16(x-3)² = 16. a) Find the center, vertices, transverse…

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Q: Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve…

A: y = xe-x , 1 ≤ x ≤ 7

Q: g(t) = t³+ t².

A: g(t)=t3+t2

Q: 2 x² e ³+1 dx

A: We do only first part of multiple questions.please re-post other parts.