Use sigma notation to write the Taylor series about I = 6 for the function. 1 Σ

Q: Let us try to find where a function is increasing or decreasing given the following.  f(x) = x3−4x,...

A: Topic:- calculus

Q: Use integration by parts to evaluate the definite integral. 8t? In(t)dt Give an exact answer

A:     ∫1e8t2lntdt=8·∫1et2lntdt=813t3lnt-3·∫t23dt1e=813t3lnt-3·t391e=813t3lnt-t331e=82e39+19=82e3+19

Q: The graph of the derivative f'(t) of f(t) is shown. Compute the total change of f(t) over the given ...

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Q: Find the inflection point of the function. (Hint:  g''(0)  does not exist.) g(x) = 4x|x|

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: First we draw a graph then find volume.  Interesting point are 0 and 1 then using limit 0 to 1 . 

Q: Find the value of the limit x² + y? lim (x,y)→(0,0) 2x + y (You can consider using the polar substit...

A: Limit  =  0 When both variable are in sum and squared form then trigonometry subsitution results in ...

Q: x3+2` dx x2 x3

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Q: Use the indicated substitution to evaluate the integral. -3 cos x sin (sin x) dx , u= sin x 3 sin (s...

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Q: In getting the derivative of a rational function, just get the derivative of

A: Topic:- derivatives   

Q: Given the function f(x) = x° + 5x*, determine all intervals on which f is both increasing and concav...

A: Given :f(x)=x5+5x4To find: All intervals on which f is both increasing and concave up.  

Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places acc...

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Q: Evaluate the indefinite integral (t)cos (t)dt

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Q: az Use the Chain Rule to find az and as for z = x2y3,x = s cos t, y = s sin t. %3D at

A: We will use chain Rule to perform differentiation.

Q: 2. Let R = {(1, b) ERX R: there is an integer k such that a – b = 2kn}. Prove that R is an equivalen...

A: us the definition of reflexive , symmetric and transitive property of relation to prove it is equiva...

Q: 25. Evaluate the following definite integral 10 a) S" V5x – 1 dx b) Sz sin 2x dx

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Q: For each item, graph the function f (x). Use the graph to estimate lim f(x), lim f(x), and lim f(x)....

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Q: S(2y + 3)?/ y+ 2 dy

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Q: y2)dx = xdy when X2 ; Y- 3

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Q: ds using the trapezoidal rule and Simpson's rule. Determine Evaluate The value of -ds is (Round to f...

A: Topic:-  integration   

Q: the cross section of a trough is a parabolic segment 8 ft wide and 4 ft deep. if the trough is fille...

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Q: The function f is shown below. What is the value of | f(x) dx? Write your -4 answer in simplest form...

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Q: do The marginal cost of printing a poster when x posters have been printed is 1. dollars. Find c(196...

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Q: Evaluate the following integrals of inverse trig functions. NOTE: SHOW COMPLETE SOLUTIONS 1.∫ sin^...

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Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -...

A: NOTE: Refresh your page if you can't see any equations. . to find the equation of velocity take der...

Q: Find the intervals in which f (x) = 2x3 + x2 - 20 x is increasing or decreasing.

A: Follow the procedure given below. 

Q: For f(x, y) = 2x3 + x²y2 - 5y3 + 10,

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Q: You deposit $2000 in an account with 5% annual compound interest. Complete the following, assuming y...

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Q: 8. 2. k(x) = %3D 1+3e-x first derivative Points of Inflection second derivative concaved up 1. conca...

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Q: C. y =1+3y tan x

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Q: In the 2000 U.S. Census, a small city had a population of 45,000. By 2010, the population had reache...

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Q: Calculate the derivative of the following function. y = (csc x+ cot x) dy dx II

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Q: A discrete random variable X has the following probability distribution: 3 4. 1 2 P(X) y 9 1. Find y...

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Q: 25 The function f is shown below. What is the value of i/ f(x) dx? Write your -4 answer in simplest ...

A: This question is related to definite integration, we will solve it using given information. 

Q: Of inter SECtion 'of thie plánes 2x+y-32=14 delete 2. Find the canation of Hhe plane Containing the ...

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Q: 2dt (t – 3)vt² – 6t +5

A: Given: I=∫2dtt-3t2-6t+5   ...1   As we know that; ∫11+x2dx=tan-1x+C    

Q: Find the critical points of the following. 1. g(w)=2w3−7w2−3w−2

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Q: Determine (in ordered pair) the point of intersection of the lines 2x – 5y = 10 and 3x + 2y = 6.

A: Intersection of two lines- Intersection point will satisfy the equation of both lines .

Q: cof z-csc z dx So 2cotzcosz

A: a detailed solution is given below 

Q: Find the volume formed by rotating about the y-axis the region enclosed by: 10y and y° = x with y > ...

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Q: 22. Find the required derivatives. a) y = (4x3 - 2x + 1)-2; find y b) x = Vy? + 1;find x"

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Q: Solve ſ cot3 4x csc² 4x dx then evaluate the answer at x=22, C=26

A: ∫cot34x csc24x dx

Q: For the following composite function, find an inner function u = g(x) and an outer function y =f (u)...

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Q: 1. Let R be a relation on the set A = {1,2,3,4,5,6,7,8} defined by aRb if and only if 2a/b?. That is...

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Q: 8. A company is increasing production of oven mitts at the rate of 4 per day. All oven mitts that ar...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 8 ka > 2sin 2 ...

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Q: Use integration by parts to evaluate the definite integral. 8t² In(t)dt Give an exact answer

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Q: 16 d.x x² Va2 + 49 Evaluate the integral: (A) Which trig substitution is correct for this integral? ...

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Q: 2t es the given condition; r' (t) =i+ te-t"j - =k;r(0) = i %3D t2+1 Vt2+4

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Q: dx 9x2 - 12x-5

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Q: Evaluate the integral 1- 25 ds VT- 25 ds

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