Suppose that T5 (x)centered at 2 for f(x)is given by Ts(x) = 3 +5(x-2) + 8(x - 2)² + 2(x-2)³ + (x - 2)5. Then, f(2)= [Select ] and f(3) (2) = [Select ]

Q: dy dv 2 Find for y = = [ √3 +4 dt. 0

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Q: O O 2x4 1,34 dx +1 NIS In[x5 + 1] + € C In[x5 + 1] + C 5 In[x 5 + 1] + C In[x5 + 1] + C

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A: Topic = Integration

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A: The graph of a function f is symmetric about the origin if             f(-x) = -f(x)

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: SS. R (x² +. tyl JA 2 SS 1 0 277 2 2 (r² cos²o +r sine)r de dr It is left as an an integral exercise

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Q: 64. The complete cardioid r = 2 - 2 sin 0

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Q: Find the general solution to the differential equation: y' = 8x + e²r

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Q: Determine whether the following series converges. 5(-1)k+1 Σ k=1 k5 Let ak 20 represent the…

A: Given: Here,            ak=5-1k+1k5 and decreasing series.  Now,…

Q: the degree of the following polynomials functions: a. f(x) = x^5  b. f(x) = (x^2)^3  c. A cubic…

A: Given the query is to find the degree of the polynomial.

Q: Find the vertex, focus, and directrix of the parabola. y² + 2y + 16x + 33 = 0 (x, y) = vertex focus…

A: The given equation of parabola is:             y2+2y+16x+33=0⇒ y2+2y+1+16x+32=0⇒…

Q: = 4 cost, Use an integral to find the area of the region bounded by the curve x = y=5sint, 0≤t≤2π.

A: SOLUTION-

Q: Find the limit. lim X→1 lim X→1 √√x² +15-4 2 X-1 2 x + 15 -4 X-1 || = (Type an integer or a…

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Q: If y = f(x), f'(x), (f(x+h)-f(x)) and slope of the tangent to the curve of f(x), h lim h→0 they all…

A: if y = f(x) Then,  By first principle of derivative

Q: Find the derivative of the function. q= 5 3 x + 6x

A: The given function q=x3+6x5

Q: Evaluate the following integral. 12 S 0 4 log 13 (x + X + 1 1) -dx

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Q: Using Trigonometric Substitution a substitution of x = 6 sin(theta) was used to solve an integral.…

A: trignometric substitution

Q: (y² - 2xy + 6x) dx − (x² − 2xy + 2) dy = 0. ANS. xy²x²y + 3x² - 2y = c.

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Q: Identify the inflection points and local maxima and minima of the function graphed to the right.…

A: Topic- application of derivatives

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A: The area of a rectangle is increasing at a rate of 4 cm/sec ? while the width of the rectangle…

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A: Topic- Equation of line through given points

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 8x…

A: Given: y=8x arccos(x-1) and point (1,4π)

Q: (1 + y²) dx + (x²y + y) dy = 0.

A: The differential equation is given by 1+y2dx+x2y+ydy = 0                               ........1 To…

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Q: Evaluate 02 3√2 0 1 3√2 0 1 |- √2 1|2 sino 4cos0 LLL rdzdrd0.

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Q: the answer

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Q: 8. Consider the differential equation e* (y - x) dx + (1 + e*) dy = 0. (a) Show that this is an…

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Q: Determine whether the given set of functions is linearly independent on the interval (-co, co).…

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Q: sinx cosx 4 + sin¹ x X dx

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Q: 8] n=1 1 n√n +1

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Q: '() = xp (x-₂x) + xp (x + xx7)

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Q: Let r(t) = t²i + t cos(πt)j + sin(ät) k, find ſª r(t) dt.

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Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.03 cm /…

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Q: f(x) = n=1 (7-2x)" 6n

A: The objective of the question is determine the derivative of the given power series.

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Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

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Q: Let r(t) = cos(t) i + 4 ln(t² + t)j + 5 tan¯¹(t) k. Find 7' (t).

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Q: at a price of $55

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Q: Question Find dy and evaluate when a (Enter an exact answer.) Provide your answer below: dy = = -5…

A: The given function is; y=(2x4-4)/(5x+1), x=-5, dx=0.4

Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]