x(2x² – 1)" dx After substitution is performed, which of the following is equivalent to

Q: d Calculate ri(t) · r2(t)] and d ri(t) x r2(t)] first by differentiating dt' dt the product directly…

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Q: Use the chain rule to find the derivative of 3(– 82° – 2=")" - You do not need to expand out your…

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Q: Maximum Oil Production It has been estimated that the total production of oil from a certain oil…

A: given : Total oil production T(t) = −1000(t + 11)e−0.1t + 11,000   Production at time t given by

Q: Determine whether the series converges absolutely or conditionally, or diverges. (-1)" n + 2 n = 0…

A: Alternating series test:∑n=0∞ (-1)nn+2an=(-1)nn+2bn=1n+2limn→∞1n+2 =0and bn+1-bn=1n+3-1n+2…

Q: Consider the function f(x) = cos(3 x). (a) Give the derivative of this function. f'(x) = | (b) Find…

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Q: Give the value(s) of x at whichf has either a local minimum or a local maximum. Give the interval(s)…

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Q: y = x/x, x = 4, and y = 0 ... Revolve the area of the shaded region about the x-axis. Using circular…

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Q: 3 (a) | (7)dx (c) dx (sin x + 1)dx (b) L (x° + 2x + 1)dx (d) 0,

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Q: 3 lim (1+ 4 x2

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

Q: Use Laplace transforms to solve the following initial value problem S y( (t) – y(t) = 8 (t) y(0-) =…

A: We need to find out laplace transform of the initial value problem, which is described in step 2 .

Q: Use implicit differentiation to find the gradient of the tangent line for xy 6xy - 2x = 9 at the…

A: topic- application of derivative

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

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Q: 7 For AABC, you are given m2C = 39°, mZB = 44°, a = 30ст. Find c. 17.9 cm 16 cm 19 cm 22 сm Previous

A: We will find the c.

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

A: topic- functions and derivatives

Q: 5. If f(x)= 5x² + 2x+1 is an invertible function, find the slope of the tangent line to f^(x) at the…

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Q: 14. The f'(4) for y = v3x2 + 1

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Q: f (x)= arcsin (x³)+ aretan (4x)

A: derivative

Q: The graph given below is graph of f '. Determine where f is increasing, decreasing, concave up,…

A: Let's find.

Q: 6- Give ā = [A, B]and b = [F,E], find VProj(b onto ā) and SProjd onto b). Resolve d into…

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Q: 15. Find x² (2x³ + 4)5 dx

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Q: Find r'(t). r(t) = (tan-(4t))i+t cos(t)j – Vtk NOTE: Enter your answer in terms of i, j, and k.…

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Q: Evaluate the definite Integral by the limit definition. Step 1 To find the deinite Integral by the…

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Q: Determine whether the sequence converges or diverges, and, if it converges, find lim an: n-00 12) an…

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Q: 5 2 dr = dr- 0 (x²+9)½ /(6+zx) 0, 's (x²+9)½ * A) True B False

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

A: topic- continuity of a function

Q: q. [sec' x/1 + tan x dx

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Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

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Q: If f(x) = /8 +r² dt , find f'(1).

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Q: 26 State the Fundamental Theorem of Calculus . you must state the first and the second fundamental…

A: On solving this we will get

Q: a) Find the general solution to the differential equation f"(x) = e8x + 3x – 1 1.

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Q: 2n+3 {a,} = 7n- 2 7n+4)

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Q: Step 3 Apply the Fundamental Theorem of Calculus, which states that f(x) dx = F(b) - Fa). Use this…

A: We can complete step 4 by the cross multiplication method.

Q: 10. Find the area bounded by 2. Hhe curves y=8x-x²0ind y=3x

A: topic - area bounded by curves

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

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Q: alculate the Laplace transform of each of the followir a. 7t b. e' sin(t) c. u(t - 3)e2

A: We can  solve 2 problems only.

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: Evaluate the following definite integral.  4

A: topic- definite integral

Q: Find curl(5z i+ 6x j+9y k). curl(5z i+ 6x j+ 9y k) = ( i )i+(i j+( i )k

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Q: ind the average value of the function over the glven Interval and all values of x In the Interval…

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Q: dv 4.)Prove that f -Incosv + Insinv + C sinvcosv

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Q: Biologists stocked a lake with 280 fish and estimated the carrying capacity (the maximal population…

A: We need to estimate the carrying capacity.

Q: 3. Let f(x) = x (x² + 1)/2. (a) Evaluate fo f(x)dx using integration by parts. (b) Evaluate f f(x)dx…

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Q: Find the angle between vector [2, −5,7] and the x-axi

A: topic- angle between vector and x axis

Q: Find the slope of the polar curve at the indicated point. TT 7) r = 5 cos 30, 0 =

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Q: 1. Find a power series representation of In(1+x²) and determine the radius of convergence. Eind the…

A: 1.

Q: 4. A cherry pie with a temperature of 120°C was placed on a table to cool in a room of constant…

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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: 3. Find the binomial series for (1+x)3 4. Use the result in problem 3 to give a power series…

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Q: 12 Let y24xー4x+3 le) Find the eauetion.of the tangent Iine to the graph of the fuuction att x-2; O…

A: We have to find tangent line

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 9, f'(9) = 5…

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