EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx 2. x²/4-x?

Q: If f(2) = 10, f' is continuous, and f'(x) dx = 20, what is the value of f(3)? f(3) =

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Q: x³dx U sing trigonometric substitution, is equivalent to

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Q: A ladder of length 4v3 metres is resting on a wall. The wall makes a 60-degree angle with the…

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Q: x = 3 sin? (2t) – 2 ;teR y =1-3 cos (2t)

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Q: Find curl (8z i + 9x j+ 10y k). curl(8z i + 9x j + 10y k) = ( i )i +(i j + ( %3D i )k

A: solution is given below

Q: 6. The tangent to the function f(x) = ke2x at x = has slope 2e. Find the value of k.

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Q: Find div F and curl F if F(c, y, z) = 10e*Y i – 9 cos yj+ 4sin? z k. div F= curl F=

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Q: 2 For the function f(x) = 2x² – 4x, evaluate and simplify. - f(x + h) – f(x) h. II

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Q: You are going to build a rectangular shed. You will put four walls around the shed and leave an open…

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Q: ..... .... .............. ............... The values y (in billions of dollars) of U.S. currency in…

A: topic- inequality

Q: Find curl (6z i + 7x j+ 3y k). curl(6z i+ 7x j + 3y k) = ( i )i + ( i j+( i )k

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Q: For the function h whose graph is given, state the value of each quantity, if it exists. (If an…

A: Given graph,

Q: Evaluate the definite integral. e18i i+ i- (*" - 1) j + k O (el" - 1) i - (e" - 1) j + - (e" - 1) +…

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

Q: 00 (n+7)! Does the series converge or diverge? 7!n!7" n= 1 Choose the correct answer below. O A. The…

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Q: Find for the parametric curve c(t) (t-1 – 5t, 41) at the point t = -2. dx (Use symbolic notation and…

A: Given problem:- Find dy/dt for the parametric curve c(t) = (t-1 - 5t, 4t3) at the point t = −2.

Q: QUESTION 5 From a list of 13 recommended stocks at your brokerage, you want to select 4 of them to…

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Q: a. Use the product rule to find the derivative of the given function. b. Find the derivative by…

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Q: Use IBP to evaluate the indefinite integrals. 1. ∫ x³sin x dx 2. ∫ sec³ x dx 3. ∫ x cot² x dx

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Q: Adjust the domain of the rectangular equation, if necessary. y = x^2-7

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Q: Given that a parallelogram is officially defined as a "quadrilateral with opposite sides that are…

A: We need to prove the property.

Q: (t) satisfies the following differential equation. P is measured in millions and t is in years

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Q: Let f a) Simplity the expression tlath), f() XRt 50C43. Using f loc)

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Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y = 9 and…

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Q: Use the indicated substitution to evaluate the integral. • 7/2 dx, x = 7 sin(0) V49 x2 (Give an…

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Q: S" cos de 4. 2 dx .2 -1 1+x² 5.

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Q: Given the vector function ř(t) = (– 3t, 5t°, 2t° + 3) Find the velocity and acceleration vectors at…

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Q: Evaluate: /x*V1-x*dx A None 3 글(1-x4) 2 +C В 3 -(1-*) C 3 (D (1-x+) +c - C 3 E 6. o+z (p*-1)- -

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Q: Refer to the graph below. Find the consumer surplus for the demand function, D, when x= 20. Hint:…

A: We have to find the consumer surplus for the demand

Q: Let f (æ) = (In(z³ + 1))". Find the slope of the tangent line at x = 1. (Give your final answer as a…

A: The slope of tangent to a curve y=f(x) at a point x=a is given by f'(a)

Q: ||r(t) x r"(t)|| ||r'(t)||* Use the formula K(t) to find K(t). r(t) = 4 cos(7t)i+ 4 sin(7t)j + 3tk…

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Q: /hat trigonometric substitution should be used to evaluate A x=3 tane B None C x=3 sece D x=3sin0 E)…

A: Solution:

Q: A tank contains 3 kg of salt dissolved in 430 L of water. A salt solution of 0.01 kg salt/L is…

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Q: S- dx x?V4-x?

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Q: One of the correct steps to evaluate x2inx x²Inx dx to yield the correct integral A x?Inx B 1 x3 dx…

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Q: Sketch the figure of the described situation in the problem and then solve. Determine the equation…

A: Tangent and normal line: At the point of tangency, the normal line is defined as the line that is…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: Given

Q: dx 2. x²/4-x² V4-x2

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Q: Find the velocity, speed, and acceleration of a particle moving with position function r(t) = (3t² –…

A: Velocity: Let r(t) denote a differentiable vector-valued function that represents a particle's…

Q: Calculate z=e^-a sin(x)+10 √y  for a=5 , x=2 and y=8 in decimal value

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Q: Find curl (3z i + 4x j+ 2y k). curl (3z i + 4x j+ 2y k) = ( Di + ( j +( )k

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Q: Describe the graph of the equation. r = (6 – 31) i – 81 j O It is a line in 2-space that goes…

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Q: у" - у'— бу %3D 2, у (0) %3D 0, y'(0) = 0

A: Given that     y" - y' -6y = 2 , y(0)=0 , y'(0) = 0

Q: Consider the following. f(x) x(x2 – 11x + 35) - g(x) = x²

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Q: Q(t) = Q0: 2-(t/140) If the amount of polonium left after 560 days is 80 mg, what was the initial…

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Q: Solve the following differential equations of 1 x’y" – 2xy' – 4y =

A: To find the solution of given differential equation.

Q: Consider the following functions. f(x) g(x) = 8 sin x = 8 cos 2x | 2 6

A: The objective of the question is evaluate the area of the given bounded region.

Q: find the inverse, domain, range, and asymptotes for F(x)=4x-1-2

A: The given function is: F(x)=4x-1-2

Q: x+dx 1.

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Q: Use a local linear approximation of the function f(x) = Vr cos[(V2x)] approximate v3.98…

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Q: Use the ratio test to determine whether the series is Converyent divorgent or 2" n! (-1)" 5.8.…

A: an=(-1)n 2n n! 5·8·11·.....· (3n+2) When applying ratio test for alternatingseries, the absolute…