Find the arc length L of the graph of r(t). r(t) = 2 cos(t)i + 2 sin(t)j + tk, 0

Q: A tank is full of water. Find the work required to pump the water out of the spout. Use the fact…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 18 – a…

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Q: Example 3 Video Example ) Find dx. 2 - 3x2 Solution Let u = 2 - 3x2. Then du = dx, and x dx = du and…

A: Solve the following

Q: Let u(æ) = sin(x) and v() = a = 18 and f(x) (*)a u (2) -| v (2) = u'v – uv f'

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Q: 7) y=-4x 8) y=7 9) y=x

A: We have to differentiate

Q: 2x + x² _ 4×-1 X-1

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Q: A rotating light is located 17 feet from a wall. The light completes one rotation every 5 seconds.…

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Q: the bot test to determine it the use tollowing series converges or diverges

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Q: SOLVE THE EQUATION. SHOW YOUR COMPLETE AND CLEAN SOLUTION. 2 (x – y) dx + dy = 0 O x + In[2 (x – y)]…

A: To solve the given differential equation.

Q: 6. Solve the following differential equations: y'=e"(1+ y* ) a. 2+(y+2)x* =0; given y(-1) = 2. b.…

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Q: Find the derivative of the function. g(t) = e−6/t4

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Q: Use long division of pol

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Q: Given f(x) = r³ – 2x2 – x + 2 on [1,2]. Verify the three conditions of the hypothesis of Rolle's…

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Q: Find the equation of the tangent line to the curve y = 6 tan z at the point (, 6). The equation of…

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Q: ner to integrate with respect to x or y. Draw a typical approximating rectangle. y -10 - 10 -5 5 10

A: We have to choose the correct option from the given options according to the given information

Q: a cost i 6. Find the moving trihedral and the curvature of R(t) a sin 2t k OE

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Q: a)Write an equation for a degree 3 polynomial that has zeros at x = -2, x = 1, and x = 4, as well as…

A: We are allowed to solve one question at a time. Kindly repost other problem in next questions. Thank…

Q: SX³V1+ 4x2 dx .3

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Q: -13x²+4x³+2x-7 x²+3x-2

A: see below the calculation and answers

Q: Evaluate the definite integral. i+e"j+t – (e~1 – 1) j + 5 i-ej+: (e – 1) i – (=" – 1) j + -1)j+극k i+…

A: We have to find the solution of  integral

Q: (ii) Hence, evaluate 37x² – 17x + 38 J, (x + 6)(x – 1)²"

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Q: Find the general solution of (3xy-y²)dx-(x²-xy)dy=0

A: As the equation is homogeneous , put y=vx and solve .

Q: dy find .2. 4 If y= 2x+ at x= 1. dx dy at x = 1 is The value of (Simplify your answer.)

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Q: (n-2n-25n2 -80n+65)+(n-7)

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Q: Consider the function f(x) = 4 – 2x", - 4 < x < 2. The absolute maximum value is and this occurs at…

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Q: The total cost to produce x handcrafted wagons is C(x)= 80 +3x -x +5x°. Find the marginal cost when…

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Q: Find the indefinite integral and check the result by differentiation. Step 1

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Q: a. Find any intercepts (list as ordered pairs). х-int у-int b. Find any critical numbers. c. List…

A: topic- functions and derivatives

Q: The graphs of the functions f and g are shown below. If u(x) = f(g(x)), find u (4). 3. 2- 2. 3.…

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Q: What is the equation of the circle with centre (,0) and radius 2? (2a- 1)2 + y? = 2 4. (2x-1)2 + y?…

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Q: (b) y = e=* + + In(3z + 1) (c) y = (cos z)° + sin(2*) (d) y = #° arcsin(2*)

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Q: Which of the following graphs represents the polar equation defined by: r = 2+2 cos 0?

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

A: Determine whether the sequence converges or diverges. If it converges, find the limit.

Q: S- |-3x cos 4x dx 3 A)- cos 42 -x sin 4x +C 16 B) cos 4x --x sin 3x + C 16 3 cos 4x - 16 cos 4x - 3x…

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Q: t-4 lim x-3-3-ax

A: We have to find out the limit

Q: Evaluate the integral (Partial Fraction Decomposition) xdx J (x² + 2)(x² + 1)2

A: ∫xdx(x2+2)(x2+1)2Substitute u=x22→dudx=x→dx=1xdu=12∫1(u+1)(2u+1)2duPerform partial fraction…

Q: Evaluate the integral 5х — 2 dx (x + 3)2

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Q: (c) Let f(x) =; for x * -K (x + K)" (i) Find f-(x). (ii) Use the result in (i) to find the function…

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Q: 2013 2009

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Q: Find the particular solution determined by the initial condition. ds 17t +7t-6, s(0)= 86 dt %3D The…

A: The given differential equation is ; ds/dt = 17t2+7t-6, s(0)=86

Q: Use the formula k(t) = ||r'(t) × r"(t)|| to find k(t). ||r(t)||* r(t) = 8 cos(7t)i+8 sin(7t)j + 3tk…

A: Let's find.

Q: 36 Use substitution to find the indefinite integral dx. (6x - 7) 36 dx = 7 (6x - 7)'

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Q: 12) y- 3x+ 2x

A: We know that ddxxn = n·xn-1

Q: (b) Determine the values of a and b that make f(x) continuous for all real x. x² – 4 x- 2 f(x) =…

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Q: Sketch the region enclosed by y = e*", y = e", and x = 1. Find the area of the region.

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Q: PART 1. Complete the table Tre Lf (x) f (x) f'(x) f'(x)dx (2) (1) f(x) = 3x* – 5x³+ 6x2 - r + 7 (1)…

A: The given function is  f(x)=3x4-5x3+6x2-x+7.

Q: f (x) = X+10 x²+3

A: The given function,       fx=x+10x2+3

Q: -ide each of the fol x-4x²+2x-3 x+2

A: Solve the following

Q: Solve: (2y cos x + sin* x) da 4 = sin x dy O y csc x + cos ¤ = O y csc x – cos a = C O y csc? x +…

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Q: For the function S-22 + 3x if z <1 f(x) = | 2x + 2 if z 21' evaluate the limit lim f(x). (If a limit…

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