lim [[ 2-y]] + x2 z-k+zk _2-4h (!) Y→-2+ _zy + [[2-y]] y² +y-2

Q: f(x)-f(a) x-a a. Use the definition mtan = lim x→a a. mtan to find the slope of the line tangent to…

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Q: Use the four-step process to find f'(x) and then find f'(2), f'(3), and f'(6). f(x) = 2x² - 9x+10…

A: Solution is given by

Q: If f(x) ƒ'(x) = | = 4x sin cos x, find Find f '(1) =

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Q: Given that f(x) = (x-7)2 and g(x) = 7 - 4x, find: a) (f + g)(-3)- b) (f-g)(-3)- c) (fg)(-3)- d)…

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Q: Find the solution of the differential equation y" — xy' + y = 0 a. y = x² b. y = x c. y = 1-x² d. y…

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Q: 3 y Find the length of the curve x = 9 + 3 4y on 3 ≤ y ≤ 5.

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Q: A certain retailers will buy 22 cordless phones from a supplier if the price is $72 each but only 35…

A: This question can be solved by applying the concept of linear equation.

Q: If f(x) = ƒ'(x) = 4x(sin cosx), find

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Q: dz dt If (z=x. y), where x = cos (t) and y = sin (t) 03. Use the chain rule method to find

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Q: ( xy² + y ² ) dy = ( x ³ y ³ + x² - y ³-1)dx

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Q: 2) Suppose that f(x)=x*(1-x) Find the maximizing value of x and what f(x) equals at that x. b) How…

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Q: Calculate the limits A) lim 818 2x²-x² +1 3 8x³+x²³+x-2 B) lim 8118 3x² + x-1 4x-7

A: Here are the solution:

Q: If g(x) = cos(x) then g'(x) = = g'(3) =

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Q: Evaluate the piecewise defined function at the indicated values. if x≤6 6x-3 if x>6 f(x) = 0 - {²x-3…

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Q: Fill in the blank for the following statements (choose FIVE only) 1- The rectangular…

A: all six are solved

Q: ) = (x + 3) can be expressed in the form f(g(x)) where f(x)

A: We have to find the function g(x) according to the given information

Q: (y) over any 173. 3/2 =(x² + 2)² y= from x = 0 to x = 1

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Q: A certain retailers will buy 26 cordless phones from a supplier if the price is $31 each but only 27…

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Q: 3-1 x2-x² - 4x +4 (a) lim (b) lim (3x³ +√9x6 - 2x³) x→ ∞

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Q: Y X arb 1.5 Lab Activity In BMX dirt bike racing, jumping high (or "getting air") depends on many…

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Q: The nuclear waste from a nuclear power plant decays at a rate of 44% each century. If 60 pounds of…

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Q: Express the domain for each function using inequality notatation. Enter "DNE" for the empty set and…

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Q: (1-x)y' = y²

A: Given Differential equation (1-x)y'=y² This can be written: (1-x)dy=y^2dx; separating the variables:…

Q: 5π Find the equation of the tangents to the curve y = sin x at x = 0, +, and 2 their tangents. Label…

A: To find the equation of the tangent.   y = sin x at x = - pi .  To find the tangency point.   y =…

Q: 6. f10e* √1+2e¹dx

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Q: Consider the function y = f(x) = x² + 4x + 4 and the x-value xo 8. (a) Find a formula for the slope…

A: Topic- slope of a tangent line we are given a function, f(x)=x2+4x+4 and x0=8

Q: Evaluate each limit, if it exists: a)lim ²-4 x-2 X-2 1-x² b)lim x-1 1-x x²-4x x=0 x(x-1) c) lim

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Q: t) Identify the type of quadric surface defined by the equation 9y²- and find all x-, y-, and…

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Q: = Find two unit vectors orthogonal to both u = (3, -3, - 4) and 7 values (no decimals). Separate the…

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Q: 65-4 52-45+16 4/ A: 1- L-1,

A: given the function in laplace form

Q: Consider the following. = a₁ 6₁ an + 1 = an + 6 Calculate, to four decimal places, the first eight…

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Q: A. FUNCTIONS, LIMITS AND CONTINUITY 1. For the function f(x) = 3× find f(x+1)/f(x-2). *

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Q: Find the limit of the following. lim 0/6 lim 9/¹ 0 sin 9- 0 0- sin 0- T 6 1 2 T 6 1 2 ...

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Q: a. Use the definition mtan lim x→a f(x)= b. Determine an equation of the tangent line at P. c. Plot…

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Q: D] A freight truck consumed 26 gallons of gasoline to cover a distance of 125 miles while going…

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Q: O 3 m/~ ~0/3 3 3 The function g is defined by g(x)==- What is the instantaneous rate of change at x…

A: Topic = Rate of change

Q: y' + y² sin x = 0 Ans: y + cos x = c

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Q: For any given base, what does 100 represent? a) The base squared -1 b) The base squared c) The base…

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Q: A hardware store purchased a tool at P20,000 per unit. At what price should the tool be sold so that…

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Q: The given table represents a pattern of exponential growth.   x      1        2          3 h(x)…

A: Topic- Exponential growth model  we are given points of a exponential function as h(1)=11.8…

Q: lim. sin(t) t =

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Q: 3) Consider the following functions: a) f(x,y)=xy. b) f(x,y)=x²y² c) f(x,y)=lnx+lny

A: As per our guidelines we are allowed to solve only 3 subparts.   Given a) fx,y=xy b) fx,y=x2y2 c)…

Q: (5, 4) and 6 = ( − 7, 8). Compute the following vector projections. Let a = proja b proj; a =

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Q: 5. A culture contains some bacteria, with the population increasing exponentially. The culture…

A: Let's find bacteria function.

Q: y²dx + x(x+y) dy=0 A xy²=c(x+2y) B x²y=c(x+2y) C D xy² = c(2xy) x+y²=c(2xy)

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Q: The given table represents a pattern of exponential growth.   x      1        2          3 h(x)…

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Q: 1. A single-lane street 10 ft wide goes through a semicircular tunnel with radius 9 ft. How high is…

A: Concept: As we know that the equation of the circle is represented by x2+y2=r2 Here y is represents…

Q: Find the solution to the given (y+x³y³)dx+xdy = 0₁

A: y+x3y3dx+xdy=0

Q: * 1. Apply the limit function to determine the derivative of y=√x - 1 Your answer

A: Please see the below picture for detailed solution.

Q: 4. Find the Laplace transform of following functions: (i) (ii) (iii) f(t) = 20 f(t) = t - 2et f(t)=…

A: Basic formulae for Laplace Transform are required.