26 State the Fundamental Theorem of Calculus . you must state the first and the second fundamental theorem of Calculus

Q: 12. The demand function for 66 piece Tinkertoy set is D(q) 750 and the supply q+1 function for…

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Q: F(x) = e2x C = 0

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Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

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Q: Indicate a general rule for the nth term of the sequence when a, = 2 and r =. 3. a, = (2)(J)*| n+1…

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Q: Finding the work done in lifting a leaking bag of cement. A bag of cement originally weighing 143 lb…

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Q: S csc-2a(seca)-da

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Q: Identify the function and interval which does not meet the conditions for applying the Mean Value…

A: We have to solve above question

Q: short

A: Please refer to the image below

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: Find the exact value of each of the following trigonometric fum 12 90 <0<180° 13 sin 0= cos 0=…

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Q: Find the nth term of the arithmetic sequence (a wh a, = 4; d = What is the nth term of the…

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Q: Consider the lines l : = 2 – y = z +1 and l2 : y - 2 3 1. Determine a direction vectors for the…

A: Consider the lines L1: x-12=2-y=z+1 and L2: 1-x2=y-2=z-33.1 To determine a direction vectors for the…

Q: Showing all work, use the method of your choice to find the volume of the solid obtained by rotating…

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Q: Answer the following questions for the function f(x) = x/x? + 1 defined on the interval – 5 <x < 7.…

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Q: 5. f(x) = (3x² + x)e5x² %3D

A: Explanation of the answer is as follows

Q: .5 2. 2. dx =D dx- (6+z*) o o (x²+9)½ 's (x²+9)½

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Q: (d) lim Use the graph of the function f to decide whether the value of the given quantity exists. If…

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Q: -2- At the point shown on the function above, which of the following is true? O f' > 0, ƒ'' > 0 Of'…

A: If the second derivative is positive then the graph of the function is concave up.

Q: Differentiate the following using implicit differentiation 3/a + V = 7

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Q: y x/x, x-4, and y =0 -2

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Q: Write the given decimal as an infinite series, then find the sum of the series, and finally, use the…

A: The sum of the infinite geometric series with first term a and common ratio r is given by…

Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: Find the coordinates at times t = 0, 5, 10 of a particle following the path a = 9+ 5t, y = 2 – 7t3.…

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Q: Find the roots Lzerel of eah tunction and State tHhe multipicty of any veputed root - 니 2x

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Q: EXAMPLE 1: Consider the graph of the function f given below. Using the given graph, determine if the…

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Q: 6. The rate of growth of a particular population is given by dp 50t? - 100t3/2, where P is the…

A: Given problem:- The rate of growth of a particular population is given by (dp)/(dt) = 50t2 - 100t3/2…

Q: V100-1000 lim y-10

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Q: The volume V, in liters, of air in the lungs during a three-second respiratory cycle is approximated…

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Q: Find the derivative of: 3 sin (– 3x). Hint: sin (x) = [sin(x)]"...so use the chain rule (twice!).

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Q: If x= tane , then dr = coso de . (1+x?)½ A True B) False

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Q: Find div F and curl F if F(x, y, z) = xªi – 2j + yzk. div F= curl F=

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Q: Determine whether the sequence converges or diverges, and, if it converges, find lim an: n-00 3 - 1n…

A: We have to find the limit

Q: In ASTR, t = 15 ft, r = 16 ft, mLS = 35°. Find the area of the triangle and round to the nearest…

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Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: The arc y = x² from (0,0) to (2, 4) is rotated about the y-axis. Find the area of the resulting…

A: We want to find surface area

Q: Find 17. d Ssin (4x) cos(4x) dx

A: Use substitution to solve

Q: Find the limit. 421 (a) lim 7+ 17 (b) lim x-0 X 3

A: Topic = Limits

Q: Integrate the following problems. Show all your work. 9. S(10xt – 5x3 + 3x)dx

A: Please refer to the image below

Q: 16. Given: [ S(x)dx=10; s(=)d& x = ? (x)dx= 3;

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Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: y =x und y = x+2 ... evolve the area about the line x 3. Using cylindrical shell method, the volume…

A: The cylindrical shell method gives the ,Volume on revolution about a line is given by…

Q: Problem 3. at a speed of 60 cm/s. Suppose the function g models the radius as a function of time t…

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Q: If f(x) = /8 +r² dt , find f'(1).

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Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

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Q: The percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid oz of whiskey is…

A: answer is in next step

Q: Find f'(2).

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Q: pind tue indefinete integral S In(s-1) ds

A: ∫ slns-1dsLet u=s-1=∫u+1lnudu=lnuu22+u-∫12u+2du=lnuu22+u-u24+uSubstitute back…

Q: FOLLOW

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Q: =

A: We will find the derivative.