A function F is an antiderivative of the function f if F'(x) = %3D for all x in the domain of f.

Q: 4. Consider the curve y=- + 2)" 0<x<1 a) Find the length of this curve b) Find the volume of the sol...

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Q: Write an equation of the tangent line to the curve f (x) = 2// + 3x at the point (4, f (4)). Upload ...

A: Here, the given equation of the curve is: f(x)=2x+3x To find the slope and the equation of the tange...

Q: B. EXACT EQUATIONS Find the general solution of the following differential equations

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Q: Find the volume of a solid obtained by rotating the region underneath the graph of f(x) = 28 – 7x² a...

A: Topic = Volume

Q: 7. In a certain country, the number of people (in millions) using their mobile phones to check email...

A: Given query is to find the derivative of the function at different points.

Q: Given the angles a, B where 0 < a, B < - which of the statements is TRUE? 4 O The angle a+B is in QI...

A: Topic = Trigonometry

Q: 5T is equivalent to 12 The expression csc 1- 2 sin? 12 1 Cos 6. - 1- cos 6. 5 2 cos? 6 - 2]

A: Topic = Trigonometry Correct option  csc5π12=21-cos5π6  

Q: 9. A lot has the form of a right triangle, with perpendicular sides, 90m and 120 m long. Find the le...

A: Given:       

Q: (») LLa (1-y? In(x² + y² + 1) dx dy 1-у2

A: Given: ∫-11∫-1-y21-y2    lnx2+y2+1dxdy

Q: dx Evaluate the integral: a4/49x2-25 (A) Which trig substitution is correct for this integral? 25 se...

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Q: A particle starts at point (1, 0, 1) and moves 2 units along the curve defined by a vector equation ...

A: A particle starts at point (1, 0, 1) and moves 2 units along the curve defined by a vector equation ...

Q: Which of the following sequences are convergent sequences? Select all that apply. 7" O an n7 1 O an ...

A: sequences are given, we have to find the convergent sequence

Q: Find the inverse laplace transform of F(s) = 6s/(s^2 + 25) + 3/(s^2 + 25) * %3D

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Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f' (...

A: Use differentiation of trigonometric function

Q: (axy-ay) dx +( 3x'y - 4x) dy = 0

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Q: Let cH)=LE?, t,6">, a) T(1) 5) K1)

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Q: find the dot product of a vector function with itself. r(t) is a curve and the magnitude of r(t)=pi ...

A: Let  u = a i^ +b j^ be a vector functionthe dot product of u with itself is given byu·u = a i^ +b j·...

Q: Use the given functions to find each of the following and their respective domains. Do not try to si...

A: given,

Q: *n/3 27. tan'x sec*x dx 28. tan (2x) sec (2x) dx /3 29. tan'x sec x dx 30. tan'x sec°x dx 31. tan'x ...

A: solve integration  

Q: What is a function, in your own words? Give an example to back up your points.

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Q: -X olx *2+2x+.

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Q: 1. Evaluate the limit of as x approaches 3. В. 3/5 x2-4x+3 A. 3/2 C. O D. 5/2 4x-x 2. Evaluate the l...

A: Note: According to our expert guidelines only first three subparts are to be answered.kindly repost ...

Q: Find one or more values of each of the following complex expressions

A: We need to compute the value of the given expression.          e2tanh-1i

Q: Differentiate the function. z = A + Bcos y

A: We know that d/dx(xn)=nxn-1 d/dx(cosx)=-sin(X)

Q: Find the horizontal asymptote(s) of the function p(z) f (x) Va(z) where p (x) = 3x? – æ – 2 and q (x...

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Q: If is the diameter of the circle with A = (-2,6) and B = (5, 4), then the center of the circle is at...

A: AB is the diameter of the circle with A=-2,6 and B=5,4

Q: 4 1-1 if I 4 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(z) = lim...

A: We have to find out limit

Q: For mumbers 9- 10. Consider the probability distribution of the number of mangoes given below. R PIR...

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Q: 5æ? about the y axis for 3 < x < 8 Find the area of the surface obtained by rotating the curve y No ...

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Q: Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (±...

A: We will find the equation of the hyperbola when vertices and asymptotes are given.Below find the det...

Q: Figure 2 shows the shaded region S bounded by the curve x = y² – 2y + 1 and the line y = 3. Find the...

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Q: What word or phrase best fits in the blank below? "If lim f(x) = L, then when x is near a the corres...

A: For limit to exist, Left hand limit (LHL) and right hand limit (RHL) both should exist and equal to ...

Q: 2) The limit below represents the derivative of some function f(x) at some number a. limh→02(2+h)^6...

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Q: 4. Consider the function g(x) = r+3° a) Find the derivative of g using differentiation rules. b) Ver...

A: The given function, g(x)=2x+3

Q: Use the definition of the derivative to find the derivative of, f(x)=6

A: topic - derivatives

Q: 2. (D³ + 3D² – 4)y = 0 -

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Q: 5. Find the linear approximation (i.e. the tangent plane) of f(x, y) = Vx/y at the point (9, 4) and ...

A: The Local Linear approximation of f at (x,y) using the partial derivative f at (x0,y0) is given by  ...

Q: Use the definition of the derivative to find the derivative of, g(x)=x3−2x2+x−1

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Q: Write a full solution  Let consider the following function: f (x) = 2(x + 1)^2  −8.  A) Find f(−2)...

A: Solution is written in step2.

Q: y = Ceax cos(bx) + C2eax sin(bx); a and b are parameters y = Ce2x cos(3x) + Cze2* sin(3x)

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Q: ст A particle moves along a straight line and has acceleration given by s'"(t) = 5t. Its initial vel...

A: To find the position function s(t) , integrate the given differential equation two times and apply t...

Q: find the equations of the tangent and normal to the curve expressed in parametric form at the point ...

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Q: Suppose R is the region bounded above  by the graph of f(x)=8x−x^2 and below by the graph of g(x)=x ...

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Q: Approximate the integral using the indicated rule. 36 0 x2 dx; midpoint rule; n = 6

A: We have to find approximate value of integral.

Q: a set of n values x1, x2.. X n has (3 standard deviation 6, the standard deviation :of n values x1 +...

A: This question is related to statistics.

Q: Complete the table below to identify the limit.Round all numbers to 3 decimal places. I – 2 lim I→2 ...

A: We have to find limit

Q: 4. Find the exact arc length over the interval. a. x= from x = 2 to x = 3 16x2

A: Solution: 4 (a)   y= x6+816x2  from x=2 to x=3

Q: B. Read and answer the problem carefully. 1. A spherical balloon is inflated with gas at the rate of...

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Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x - ...

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Q: Let f(x) = V-14 – r and g(x) = z - 9x. fog= The domain of fogis:

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