3. Find the average rate of change of the function f(x) = sin x, [0, t/6] over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.

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A: Explained below 

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A: Given query is to find integral.

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A: Given query is to find the value of the integral.

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A:

Q: Consider the following function. y3D - 2x + 2 (a) Find y' = f'(x). (b) Find the critical values. (En...

A: ANSWER: As per guidelines we can do only first three subparts , the solution is given below : 

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A:

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Q: lim 2 tan 2/ TC 2. 8IN

A: Solving the problem by finding the value of the limit.

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A:

Q: 13 What is the Maclaurin series of 1+x 8. Σ (Type an expression using n and x as the variables.) n3D...

A: I am attaching image so that you understand each and every step. In maclaurin series put a=0 ,k=0,1,...

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A: Given query is to find the integral converges or diverges.

Q: Use the Integral Test to determine whether the infinite series is convergent. n2 Σ n=19 (n³ + 3)7 To...

A: ∑n=19∞n2n3+372We need to find the given series converges or diverges

Q: Given the triangle below, find the angle 0. 15 10

A: Given that:                          

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A:

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A: Given that: y=x2

Q: Express w as a linear combination of u and v: ? = (4,1), ? = (−2, −1), ? = (2, −2)

A: Let w = (4,1) u = (-2,-1) v=(2,-2) we can write this as: u-21 + v2-2 = 41   -2u + 2v = 4 u - 2v = 1 ...

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation an...

A:

Q: 7. Find T, N, ar, an at t=n. r(1) = 4cos(1)i–4sin(r)j-3rk

A: Tt = r'(t)r'(t) and N(t) = T'(t)T'(t) aT = r'(t) .r''(t)r'(t) and aN = r'(t)×r''(t)r'(t)

Q: Find the equation of the tangent line on x2 + sin y – ry? = 4 at (2, 0). |

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the first partial derivatives of the function z = (2x + 3y)10.

A:

Q: 5) lim f(x) x--2

A:

Q: Show that V is not a subspace of R°: V is the set of all (x, y, z) such that x + y +z = 3

A:

Q: • If we did not have logarithmic differentiation, what rules would we need to use to find the deriva...

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Q: Find the derivative of the function. y = a6 + cos6 x y'(x) =

A: Given

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A: The objective is to sketch the graph of f'.

Q: 00 Does the seriesE(- 1)"n³ converge absolutely, converge conditionally, or diverge? n= 1 ... Choose...

A: Given series is  ∑n=1∞ -1nn323n To determine whether the series converges absolutely, converges cond...

Q: az and əs az e the Chain Rule to find for z = x²y3, x = s cos t, y = s sin t. at

A: We have to find derivative by chain rule

Q: Find the indefinite integral in each of the following. Show all necessary solutions. (2x – 3)dx 2. V...

A: Given :∫(2x-3)dxx2+2x+2

Q: Sx² sin x dx

A:

Q: 2. Let E be the piece of the cone z = 'outward' (pointing away from the z-axis) normal. Let F be the...

A:

Q: Can you please help with the assignment questions. Thank you

A:

Q: dw for w = dt xez,x = t2,y = 1– t,z = 1+ 2t. e the Chain Rule to find

A: Given query is to find the derivative using chain rule.

Q: Use Integration by parts to aompute the ntegral from! (4x)dx and 3 Inxdx

A:

Q: If s(t)represents the position of a function, in metres, at time t, in second what does the expressi...

A: s(t) represents the position then  limh→0s(3+h)-s(3)h represents the velocity at time t=3 seconds Co...

Q: A cylinder has a height equal to its radius. Find the rate of change of volume V with respect to rad...

A:

Q: Find the indefinite integral in each of the following. Show all necessary solutions. 3. sin ? x cos'...

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Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation an...

A:

Q: The graph of y = \xl, shifted 9 units to the left Oy = |x - 9| O y = |x| + 9 Oy = |x + 9| Oy = Ixl y...

A: If a function is given as y=f(x), then To shift it up wards by k units we use y=f(x)+k To shift it d...

Q: 1. Find lim,→0 k e'

A:

Q: A cylindrical tank with radius 6 m is being filled with water at a rate of 2 m3/min. How fast is the...

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Q: 1+x2+y2 Determine the set of points at which the function F(x, y) = is continuous. 1-x2-y2

A: In this we have to check Discontinuity of equation. 

Q: Find lim_f(x), if it exists. If it does not exist, explain why. X--4"

A: Follow the procedure given below.

Q: [sin (21x) dx

A: ∫sin4(21x)dx Note- sin2x=1-cos(2x)2 and cos2x=1+cos(2x)2

Q: Write -4 +3i in polar form A) 5 L 38.87° B 5 L<216.87° (c) 5L<323.13° D) 5 L<143.13°

A:

Q: Use the Integral Test to determine whether the infinite series E 41 is convergent. (Use symbolic not...

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A:

Q: Find an equation of the tangent line to y = 5 tan(x) at x =

A: Given problem:- Find an equation of the tangent line to y = 5tan(x) at x = π/4 .

Q: Show that V is a subspace of R³: V is the set of all (x, y, z) such that z = 2x + 3y

A:

Q: sin(tan-1))

A: SOLUTION-

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A: Given:   Graph is given