Directions: Solve the following using the theorems on differentiation. 1. Evaluate x5dx 2. Evaluate [ 4 dx 3. Evaluate I (x² + x³)dx 4. Evaluate Í vVx (x – 4)dx

Q: 1- P is equal : a) 1 b) 120 c) 5 2- C is equal : a) 455 b) 544 c) 4542.

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Q: Given the rate law and table below, what are the values of m and n? Rate = k[A]m[B]" [A] (M) [B] (M)…

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Q: f fcx) = 5 Ccor"2x) 131

A: The objective of the question is determine the derivative of the given function.

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(t), cos(3t), cos(t)) when…

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Q: A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from…

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Q: height. What is the largest volume bag of this shape that you can carry on a flight? (Round your…

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Q: 3-A coin is tossed 3 times the probability that all 3 tosses are tail equal a) b); c); d) 9.

A: Our Aim is to calculate the probability of flipping a coin three times andgettiing 3 tails.

Q: Calculate the derivative by expanding or simplifying the function. 1- 2(19t) s(t) (19t)l/2 (Use…

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Q: A Norman window is constructed by adjoining a semicircle to the top of a rectangular window, as…

A: Perimeter of Norman window(P)=Perimeter of rectangle(P1)+Perimeter of…

Q: 4.lim 1252x-7+2 Sーズ 5. lim e*+1 X-4

A: Let's find.

Q: Publishing The following table shows the results of a survey of 500 authors by a publishing company.…

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Q: An object moves along a coordinate line with velocity v(t) = 1(6 - 1) units per second. Its initial…

A: Solution:  To find the position of the object at a point, we must find the position function, which…

Q: What is the volume of the solid formed by revolving the region bounded by 6y =x2 and 6z ? %3D %3D…

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Q: B a A b Note: Triangle may not be drawn to scale. Suppose c = 5 and A = 70 degrees. Find: a = b = В…

A: Solving the problem by finding the missing values of the triangle.

Q: 4.two die are tossed, the probability that the sum of two faces will be 4 11 d) 3 a) 72 b) 12

A: Probability

Q: Find all the derivatives of f, given f(x) = x8 – 5x7 + 4x6 – nx* + 3x³ + 11.

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Q: A mass weighing 32 pounds stretches a spring 2 feet. Determine the amplitude and period of motion if…

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Q: The equation y²(y²-4) = x2(x²-5) is known as the devil's curve. Give an equation for the tangent…

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Q: 13. sec*0 sin 8 de

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Q: Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in…

A: From the graph the zeros are -2, 0, 3.The equation of the function is given…

Q: Find the limit. lim (t i – 3 j + t² k) t→8 Exact number, no tolerance. lim (1 i– 3 j+? k) i+ i j+ i…

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Q: An iron block weighs 5.2 N and has a volume of 272 cm³. What is the density of the block in kilogra…

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Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=…

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Q: Evaluate: S Vx(x – 5)dx

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Q: 2 sec" x AX JS -sec? x

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Q: Approximate the local minimum value of the function given below. Use Newton's method with the…

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Q: Jse the (first principles) definition of the derivative to find g'(x) if g(x) = I+ 2

A: Explanation of the answer is as follows

Q: question uppose f is continuous on [6,9] and differentiable on (6, 9). If 9 < f'(x) < 14 for all…

A: Given the query is to find the range of f(9)-f(6).

Q: 9 Derivative of fi») 1x 4 . 5. 1 f) 1x1cosx, fird f'n)

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Q: y' = xy – Vx

A: Solving

Q: Find y' if x Y= y* %3D

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Q: Given: re + In(x - y) xe*? Find dy/dx. 2ry(z=y)+z* 1+(z=v}(2»² +1)e| dy dr 2r(z-y)-z1z…

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Q: 33. f'(t) = sec t (sec t + tan t), -/2<t<T/2, f(T/4) = -1 %3D %3D 34. f'(x) = (x + 1)//x, f(1) = 5…

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Q: Find the average rate of change of the function from X1 to X2 Function x-Values f(x) = x2 - 4x + 6 X…

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Q: Find the indefinite integral and check the result by differentiation. S f (x) dx, where f (x) =(/¤-…

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Q: Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in…

A: Consider

Q: Find the function F that satisfies the following differential equations and initial conditions.…

A: Given,  F'''(x)=6x, F''(0)=0, F'(0)=1, F(0)=1

Q: Let f(x) = -0.4x² + 9x-12. Find the x-coordinate of the vertex. Round your answer to 2 decimal…

A: Giveen query is to find the x coordinate of the vertex.

Q: Find the exact length of the polar curve. r = 6 sin ?,    0 ≤ ? ≤ ?/3

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Q: Q(x) = Jx + Vx + Vx + ·…

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Q: Demand for the latest best-seller at OHaganBooks.com, A River Burns through It, is given by q = -p2…

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Q: A radio transmission tower is 535 feet tall. A guy wire is to be attached 6 feet from the top and is…

A: Given problem:- A radio transmission tower is 535 feet tall. A guy wire is to be attached 6 feet…

Q: (х - 1)(х - 4) 38. у- (х - 2х - 3)

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Q: y = e2a %3D

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Q: Solve the value of t using quadratic equation (unit must seconds). Include the units while solving.…

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Q: S The flux is

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Q: If Lpl=)dz = 7 and p(z)dz = 9.5 what does the following integral equal? p(z)dz = Question Help: D…

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Q: 1 3. (x+1)(x²+4)² dx

A: The given integral is  1/[(x+1)(x2+4)2].

Q: 2. Use the Laplace transform to solve the initial value problem y" + 4y' + 5y = 2, y(0) = -2, y'(0)…

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