Let f(t)=(t^2+4t+8)(2t^2+5)  find f'(t)= find f'(3)=

Q: 2ydx + (x x³y³) dy = 0

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Q: Question Let h(x) = f(g(x)). If g(5) = −3, g'(5) = −4, f(-3) −4, ƒ(−3) = −1, and f'(-3) = -5, find…

A: Let hx=fgxIf g5=-3, g'5=-4, f-3=-1, and, f'-3=-5, then to find h'5.

Q: A closed box is in the shape of a rectangular solid with dimensions x, y, and zin inches. Suppose…

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Q: 1. [e²y ycos (xy)] dx + [2xe²y xcos (xy) + 2y] dy = = = 0

A: According to guidelines I can only solve first question ,rest can be reposted.

Q: 2. Given: f(x)=√x+2 and g(x) = x² – 3x a.) solve: (gof)(7) b.) Find the domain of f, domain of g,…

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Q: If 1 f(x) = coth-¹√√x² +5 then f'(x) = 0

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Q: lim 8e +71-8 2e¹+3r-2

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Q: Question Determine whether the series below is a geometric series, a p- series, an alternating…

A: The given series is cos(pi n)/(6n), n from 1 to infinity.

Q: Find an nth degree polynomial function with real coefficients satisfying the given conditions n=3…

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Q: Find the second-degree Taylor polynomial for f(x) = 5x² − 7x + 6 about x = 0. P₂(x) = What do you…

A: To find the second‐degree Taylor polynomial for fx=5x2-7x+6 about x=0.

Q: What is the equation of the tangent line to the curve of y = A 2x+9y+1=0 D. 9x+2y+1=0 B. 2x-9y-1=0…

A: Topic = Derivative Correct Option = C

Q: Given that; f(2)=2, f'(2)-3 g(2)=6, g'(2)=4 Calculate the following (fg) 2= (f/g)'(2)= (g/f)'(2)=

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Q: The area of the region inside r= 2 + sin and outside r= 2-2 cos 0 is given by

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Q: Sketch the situation if necessary and use related rates to solve. 1) Two buses are driving along…

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Q: Use implicit differentiation to find the equation of the tangent line to the given equation at the…

A: When the slope is infinte then equation of the tangent line is a vertical line x=a where (a, b) is…

Q: 1. Use logarithmic differentitation to find dy dx y = 2 given th tan¹ x cos (csc-1x) sin 2. Find the…

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Q: When a quarter is tossed four times, 16 outcomes are possible. HHHH HHHT HHTH HHTT HTHH HTHT HTTH…

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Q: Find f'(9) if f(x) = 7x² +6x + 2 √x f'(9)=

A: we know, ddx(xn)=nx(n-1) for any real n

Q: 5. Prove that, for n> 1, n

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Q: Write the integral as a sum of integrals without absolute values and evaluate: ƒ³ |x³| dx : =

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Q: y=x^2, y=x^3 between x=0 and x=2

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Q: I If f(x) = = √² (1²³ + 3t² (₁ (t³ + 3t² + 5) dt then

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Q: Leta = (5₁5) and b=<3₁-5) SO Why that Ba Sa+t6=<-4₁-207 S= +=D]]

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Q: Let P and Q be polynomials. P(x) 818 Q(x) if the degree of P is (a) less than the degree of Q, and…

A: Given query is to find the limit of the expression.

Q: f(x) = x² - 11x + 30 g(x) = x - 5 (f+g)(x) = (f- g)(x)

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Q: Solve the equation using the quadratic formula   6x squared + 10x +2 = 0

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Q: 6. Consider the surface in R³ defined by x² + y² - 2z² + 6x - 8z = 7. (a) This surface is a quadric…

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Q: Find the indefinite integral. (Use C for the constant of integration.) √³x (3) dx Need Help? Fland…

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Q: Determine the location and value of the absolute extreme values off on the given interval, if they…

A: Concept: The slope of a function can be found in its first derivative. The slope of the curve grows…

Q: Sketch the graph of an example of a function f that satisfies all of the given conditions lim f(x)…

A: Please see the below picture for detailed solution.

Q: Find the derivative of the following functions using limits. 1. f(x)= 3x² + 4x-5 2. f(x)=x³2x²+x-3…

A: The given functions, 1. fx=3x2+4x-52. fx=x3-2x2+x-33. fx=x-12 We have to find the derivative of…

Q: Consider the following function. g(x) = 3x³ - 8x Find the first and second derivatives of the…

A: Consider the following function.gx=3x3-8xTo find the first and second derivatives of the function.To…

Q: 0 Exercise 7 Limits The following graph of the function f satisfies limf(x) = 2 . For & = 3 find a…

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Q: I dont understand what is written. Can you write in another way or atleast have spaces in between…

A: Here we have to determine the sum of convergent series.

Q: Use the binomial theorem to expand the following: (a) (x + 2y)* (c) (3x + 1)4 (b) (x - y)6 (d) (x +…

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Q: First find f' and then find f. f"(x) = 4x − (9x³+x²) + 10, ƒ'(1) = 5, f(1) = -8. ƒ'(x) = f(x) = ← FI

A: To find the derivative and the function from its double derivative.

Q: Find the critical numbers of the function f(x) = 4x5 + 25x¹ - 20x³ - answers to three decimal…

A: Given, f(x)=4x5+25x4-20x3-5

Q: Find an nth degree polynomial function with real coefficients satisifying the given conditions n=3…

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Q: Given 2y-√x-z+2√-5y-4z = -5, calculate Provide your answer below: || dz dx

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Q: Question If r(x) = ln Select the correct answer below: O r'(x) O r²(x) O r'(x) = = (32² +2+3), find…

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Q: Consider the function f(x) = 4x - cos(x) +5 on the interval 0≤x≤1. The Intermediate Value Theorem…

A: Given function:- fx=4x-cosx+5

Q: 2y(x+y+2) dx + (y²−x² - 4x-1) dy = 0 ; y(0) = 1

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Q: Given the scatter plot shown, determine if the correlation is positive, negative, or if there is no…

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Q: Find the equation of the tangent line to the curve x² + y² + 2x + 1 = xy-8y at the point (-1,-9).

A: Given equation of the curve is  x²+y²+2x+1 = xy-8y We have to find the equation of tangent So slope…

Q: A function and its graph are given. Use the graph to find each of the following, if they exist. Then…

A: Note: Since the student has posted many sub-parts of the question and does not mention any specific…

Q: 1. Calculate ›(3) (52 (a) (8) (b) (8) (52) (52)

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Q: Given that; f(2)=2, f'(2)=3 g(2)-6, g'(2)=4 Calculate the following (fg) 2 = (f/g)'(2)= (g/f) (2)=

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Q: The arc length of one petal of the rose r = sin 30 is given by 1 73 2 S 2/³ TT 1 ·풍 2 S sin2 0+9…

A: We know  Length of arc length in a,b=∫abrθ2+r'θ2dθ

Q: S S cos(x)√9+ cos²(x) arcsin (y)

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Q: Solve the quation x cubed - 13x squared + 47x - 35=0 given that 1 is a zero of f(x)=x cubed - 13…

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