Find the derivative of the following, using first principles a) 2x2 b) x3 c) 8-x2

Q: في Lim X-1 X1 X²-1

A: Hint : Factorise denominator

Q: Find the following limit. Answer as a fraction or integer (no decimals.) x² x +9x-22 x²-4 lim X-2 -

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Q: What is the general solution to the the differential equation3y" - y'- 2y = 10e *?

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Q: 1 Find the Domain and Range for y = 1-√5-x Graph and find the domain and range for y = sin²x + 1

A: 1) The given function is: y=11-5-x

Q: 25. Sa 2x²-10x +4 (x + 1)(x-3)² dx

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Q: 2-x x² if x - 2 Calculate the following limits. Enter "DNE" if the limit does not exist. f(x) = Let…

A: we will find the limit.

Q: Given the graph of f(x) = √√x as shown, graph the function 5ƒ(x) – 5. -7 -6 -5 -4 -3 -2 -1 7- 6 5+…

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Q: 1. The graph of f "(x) is continuous and decreasing with an x-intercept at x = -3. Which of the…

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Q: (a) Find a vector parallel to the line of intersection of the planes -x + 3y + 4z : 0 and -x - 3y –…

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Q: Use a graphing calculator to graph the equation in the given viewing rectangle. [-50, 50] by [-0.2,…

A: Graph of the function is given as below,

Q: C) g'(x) = 3x²; g'(1) = 3 D) g'(x) = 3x2 + 5; g'(1) = 8 mits to find the derivative function f' for…

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Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

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Q: -1 If cot (sin-¹ √√1-x²) = sin (tan¯'(x√6)), x ±0 then the value of x is.......

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Q: 2. In 2000, Morgantown's population was 26,800. It's population increases by 1.2% each year. a.…

A: Solve

Q: Kendra bought 188 donuts for $160. Her profit was $40 once she had sold 100 donuts. Which equation…

A: Find profit

Q: Express the following functions in the form utiv • f(Z) = ln (1+z) P

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Q: mation 9. y'-y = 2te²¹, y(0) = 1 2

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Q: sin 3x cos 3x (cos 3x + 1)² dx 19) f 22) fex√3-4e2x dx 20) f ITV In x dx 21) f x√4 lnx-1 23)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: b) Calculate the following definite integral: [*(√x - 3) dx

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Q: question 21. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

A: We will find the required.

Q: Find the solution of the differential equation (6x² − y + 3) dr+ (3y² - x - 2) dy=0 1 O x + O 2x³ O…

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Q: a) Find the limits of the following functions: 1. sin 2x lim- x-2x²+x lim √x² +12-4 x-2

A: SOLUTION-

Q: 3. Doubling time is the amount of time it takes to double an initial deposit. You deposit $20,000 in…

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Q: 2. Verify that the function is solution to the given differential equation. et 1+ et d.P dt =…

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Q: What are the steps to factor x3-3x-52

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Q: Find  f(a), f(a + h),  and the difference quotient  f(a + h) − f(a) h,  where  h ≠ 0. f(x) = 6x3…

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Q: 4. Half-life of a substance is the amount of time it takes to reduce to half of its original amount.…

A: We have to find the time and remaining amount of carbon-14.

Q: Which of the following is/are signified by lim f(x) = ∞00? I a As a approaches a, the value of f(x)…

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Q: Solve for a. 8. 9a 16 - a² = 9. 54 = a4 10. a² - 16 = 32

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Q: For each statement,write true or false {0,2,6}={6,2,0} {2,3,4} =[2,4] {XER:0≤x≤6}= [0,6]…

A: We will  state whether the statement is true or false.

Q: For what values of a and b is the following function continuous at every x? - 10 f(x) = axb 4 x≤ -3…

A: Function to be continuous at point x = a, it must be defined at that point.

Q: YA -3 x (a) If f is increasing on an interval, then the y-values of the points on the graph [rise…

A: Given graph of function is

Q: C. Find the standard form of the equation of a circle given the following conditions. 10 10. Passes…

A: We can solve it by various method but i solved it as shown below.

Q: Write an equation of the plane with normal vector n (7,5, -4) passing through the point (1, −5, 1)…

A: Given; n=<7,-5,4> Point (1,-5,1).

Q: im (x²-C² if X<4 1 f(x) = {(x+5 x²-c² (x + 5 if x = 4 lim

A: Given:-x2-c2   if x&lt;4cx+5    if  x≥4f(x) is continuous at x=4solution:-if f(x) is continuous at…

Q: Find the limit. lim √x+15 cos (x+4) X→-4t lim √x+15 cos (x + 4) = X--4t (Type an exact answer, using…

A: We need to find the limit of the given function as x approaches the value -4π. For all x≥ -15 the…

Q: A cell phone plan has a basic charge of $30 a month. The plan includes 400 free minutes and charges…

A: Given problem:- A cell phone plan has a basic charge of $30 a month. The plan includes 400 free…

Q: For each function below, find the derivative. DO NOT use decimals in your answers. If f(x) = 2x5…

A: Here we have to find the derivative of functions.

Q: please

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Q: 2) Consider the function g(x) = 5 + 6x²-5x-1 3x³-4x+1 a) Find the Limit of g(x) as x approaches…

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Q: Find the decomposition a = ªb + ªь with respect to b if a = (x, y, z), b = (-1,-1,-1). (Give your…

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Q: Use function composition to determine if f (x) ar (a) Yes, they are inverse functions. (b) No, they…

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Q: 43. YA 3 -1 y=2x L (3, 3) 3x

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Q: Given the two complex numbers: 2₁ = 2 + 4i and Z₂ = √5 -3i 1) Find the value of the complex number…

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Q: Q. 3. a) Find first and second derivatives of the following functions: +7x y=cot(3t-1) 201

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Q: Determine the point(s) at which the given function f(x) is continuous. f(x)=√6x +30 Describe the set…

A: We have given function  fx=6x+30 Function will be continuous if  6x+30≥0 6x≥-30 x≥-306 x≥-5 Interval…

Q: 3. lim_ f(x) = X-3- lim f(x) = X-3+ lim f(x) = x-3 f(3) =

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Q: Assume that is an acute angle. If sec8=6, find the exact value of sin 8. Write your answer as an…

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Q: Given x and f(x), fill out the rest of the table. X -2 -1 f(x) f(x) - 1-6 f(x - 1)-7 -f(x) 5 f(-x)…

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