df-1 For the function y=f(x) = x² + 2x - 6, x> -1, find dy (ƒ-¹)'(1) = y=1

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A: The given system of linear equations,The aim is to sketch the linear equations and find their…

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Q: Suppose we know that y = 2z4+3 z³ - 16 and x = 2 t² - 3 t-4. Compute the following quantities: da…

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A: A dietician is planning a snack package of fruit and nuts. Each ounce of fruitwill supply zero units…

Q: Answer these following For B try by first using properties of integrals A Sh(x)dx = 214. BS₁,…

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Q: USE INTEGRATING FACTORS 1. Find the General Solution: Answer is already given. 22. y'= 1+ 3y tan x…

A: The given differential equation is; y'=1+3ytanx

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Q: Determine the second derivative of the function: g(x g(x) = ex X

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Q: In your own words, describe the limit of a function y= f(x) as x approaches c.. The notation we use…

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Q: a. Use implicit dy dx b. Find the slope of the curve at the given point. 13. x4 + y4 = 2; (1, −1)…

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A: Given that an object travels with a velocity function given by

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Q: Find the indefinite integral. (Use C for the constant of integration.) 3t | vi √ 1 - 9t4 dt

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Q: If the expression √x² Ox=2 tan 0 Ox=2 sin 0 - 4 occurs in an integral, what substitution might you…

A: Explaination of the answer is as follows

Q: b) We want to build a container in the shape of a cylinder and it needs the materials shown below.…

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Q: Consider the following function: f(x) = (x+3)2 (a) Express the derivative of f(x) at a point x = = 5…

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Q: USE INTEGRATING FACTORS 1. Find the General Solution: Answer is already given. 4. (y + 1) dx +…

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Q: Determine the derivative of the following function. f'(x) = f(x) = (x7 +19)7

A: Given,

Q: Express the sum xx²x³ + x² + x5-x-x² + x³ + ... 4n 4n-1 in terms of geometric series (hint: group…

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Q: At a parking lot, the attendant can wait on 68 people per hour. If people arrive randomly at an…

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Q: Find the solution of the constant coefficient differential equation y" - 10y + 29y=0 y'(0) = -47.…

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Q: Evaluate each limit analytically. - (a) lim sin(x + h) – sin(x) h→0 h (b) lim h→0 (c) (d) lim h→0…

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Q: Determine lim f(x), lim f(x), and lim f(x), if it exists. X→c* X→C X→C c=4, f(x) = lim f(x) = 5 x→c*…

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Q: Use the quotient rule to differentiate the function f(x) = f'(x) = x-3 -2x+2

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Q: Practice 2: The graph of the function f(x)=arctan x -20 -10 TT -TT/2- 0 -TT/2 -TT 10 is given below.…

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Q: Differentiate the following function with respect to : f(x) = √4+x² 5x f'(x) =

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Q: Use differentials and the graph of f to approximate the following. (Round your answers to three…

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Q: The derivative of y = cos x is y' = - sinx. With that in mind... What is the antiderivative of f (x)…

A: Defination - Antiderivative is a function that reverse what the derivative doesIn other words…

Q: 5л Find the secant (if it exists) of the angle = 4

A: The aim is to find the value  for

Q: Find the following limit or state that it does not exist. lim X→1 X-1 Select the correct choice…

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Q: Practice 6: Use forced factorization to find the following limit. lim Practice 7: X+2 √9x¹² +1 2- X…

A: The given limit

Q: Differentiate the function. y = 1 (5x – 16)2

A: Given,

Q: Find the solution of the differential equation y" - 4y + 4y= 0 satisfying the initial conditions…

A: The given initial value problem .The aim is to find the solution to the IVP.

Q: Evaluate π [ -πT cos² (5x) dx.

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Q: Practice 1: Given S(x)=2x+3 a) (fog)(x) 4- x and b) The domain of fog g(x)= 6 x+1, find each of the…

A: given functions

Q: Practice 2: Use the definition of derivative at a number a to determine whether f'(3) exists when…

A: By using the definition of derivative at a number , to determine whether  exists when .

Q: Find the directions in which the function increases and decreases most rapidly at P0. Then, find the…

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Q: Set up an integral for the area of the surface obtained by rotating the given curve about the…

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Q: dy dx y = - 2x6 Find = 5 dx

A: Given, we know

Q: At what point is the tangent line to the curve y³ = 2x² perpendicular to the line x+y=2=0? NOTE:…

A: The given line is,The coefficient of x is -1 which means the slope of the tangent line is -1The…

Q: The value of a particular item can be modeled by P(t) = Po(a) where P is in dollars and t is the…

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Q: Do not use technology. Consider the following table. (a) If h(x) = h'(2) f(x) g(x) X 2 5 f(x) f'(x)…

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Q: 7. A thermometer reading 75°F is taken out where the temperature is 20 °F. The reading is 30 °F…

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Q: the altitude of a triangle is increasing at a rate of 2cm/min while the area of the triangle is…

A: The altitude of a triangle is increasing at a rate of 2cm/min while the area of thetriangle is…

Q: Evaluate the integral: Tan ( 1 ) + C 3 9+x2– arctan| ○ In (9+x²) + C 1 ( 3 ) + C In(9+x2) — arctan|…

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Q: 6- x - x² if x ≤ 4 if x > 4 2x - 3 Calculate the following limits. Enter "DNE" if the limit does not…

A: we are given the piecewise function and we need to find out the limits given.

Q: What is the antiderivative of f(x) = ? O F(x) does not exist O F(x) = (1/x)² + C O F(x) = (1/x)⁰ + C…

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