1. Find all values of k for which the function r2 _ 52 – 6 - 2x - 4 is continuous at x = 2. f(x) = 2k²-k if x # 2, if x = 2

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Q: What are the three ways a function is not different at a point x=a? ( sketch the graph for wash…

A: Guven question:- What are the three ways a function is not different at a point x=a? ( sketch the…

Q: 1. Discuss the monotonicity (i.e. identify the intervals of x over which the function is increasing…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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A: To prove that, a→+b→·c→=a→·c→+b→·c→ for vectors a→, b→, c→ in V2.

Q: Find lim f(x) and lim f(x) for the given function and value of c. x-c* |x+51 X+5' f(x) = (x+7)- x-5+…

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Q: K Find the domain and range of the function. f(x)=√√7x+14 The domain is (Type your answer in…

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Q: 2.) dy dx 1 x²+1

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Q: Solve the differential equations. 3. dr dt + KT-100k,

A: To solve the differential equation

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A: The equation of the curve is given by y = 5x-2x The point on the curve is given by x0, y0 = 1, 3…

Q: Let L be the line passing through points (-2, -5) and (3,4).  1. Find the general equation of the…

A: Let L be the line passing through points -2, -5 and 3, 4.1 To find the general equation of the line…

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Q: The population of a town is increasing at a rate given by P′(t)=48e0.012t​, where P is the…

A: see below the answer and calculation As per Bertleby guideline we have to solve only first question.…

Q: Graph the piece-wise function below. Be sure to inclu closed or open dots, but only at breaks in the…

A: The given function is  f(x)=-x if x<4 x-4  if x≥4 Draw the graph of the function.

Q: Find the curvature of the curve defined by r(t) = e²ti + 3tj 12e2t K= (lett +9) Evaluate the…

A: Find the curvature of the curve .

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Q: A business has found that it can sell 660 items if it sets its price to $63.02. However, if it…

A: let x be number of items sells and p be price of function

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Q: Prove, using the formal limit definition of the derivative, that if f(x) = then f'(3) = - 1-2x x3 s…

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Q: A can of soda is placed inside the refrigerator. The soda has an initial temperature of T = 70°F.…

A: #4

Q: At what points is the function y = x+3 x²-11x+24 continuous? 1 Describe the set of x-values where…

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Q: Let (sq. rt of 11, 5) be a point on the terminal side of  θ. Find the exact values of   a. cosθ…

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Q: Your monthly profit (in dollars) from selling magazines is given by P = 2x + √x where x is the…

A: Your monthly profit in dollars from selling magazines is given by p=2x+xwhere x is the number of…

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Q: Find the fourth derivative of f(x)=3x^−2

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Q: please solve using classical method and find its particular solution and homogenous sol. And try to…

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Q: Question Suppose that the piecewise define function f is defined by f(x) = Determine which of the…

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Q: Question Using Desmos, plot the point (-1,7) in the polar plane. Provide your answer below: 6 TT 4…

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Q: Question If f(x) = f ³ dt, find f'(x). 73

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Q: The total cost (in dollars) of producing x food processors is C(x) = 2200 + 90x−0.5x². (A) Find the…

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Q: Find r(t) u(t). . r(t) = (5t4)i ³j+2k u(t)= t²i4j+t³k r(t)u(t)= Is the result a vector-valued…

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Q: 2. Prove d dx :(arctan x) = 1 1+x²

A: To prove:- ddxarctanx=11+x2

Q: (d) Graph f(x) = 9x on the window [-9, 9] by [-9, 9]. Do you see why the slope at x = 0 does not…

A: Slope of a function y=f(x) at a point (a,b) is given by   m= dydxx=a

Q: Use the definition of derivative f'(x) = lim h→0 f(x+h)−f(x)/h to find the derivatives of the…

A: Here is the solution:

Q: Find the solution of the differential equation (1 + y²)dx + (1 + x²)dy = 0

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Q: For the given function f(x) and the given values of c and > 0, find L = lim f(x). X-C Then determine…

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Q: Prove that lim 1 H 101H 818

A: We have to prove that  limx→0- 1x → -∞.

Q: Solve the differential equation. 6y¹ = ex/6 + y A) y = B) y= xex/6 + cex/6 6 D) y = XEX/6+2 6 Ⓒ y =…

A: Solution of the given differential equation is as follow

Q: Solve the differential equation. dy + 5y dx = e-5x dx A) y = 5x + ce-5x B) y = e-5x (x + c) (C)…

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Q: Given a triangle PQR with vertices P(3,-1,4), Q(2,1,5), and R(5,0,-2), (a) Find the angle at vertex…

A: I am attaching image so that you understand each and every step.

Q: Consider the curve r = (e-4t cos(-t), e4t sin(-t), e-4t). Compute the arclength function s(t): (with…

A: To find the Arc length of the function.

Q: Suppose that f(x) = C 4x-8 Then, The domain of f is {a E Rx # Number f-¹(z) = } an and

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Q: The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. 4√5-4 f(x) C = =…

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Q: Find the equation of the line L that passes throught point P( – 6, 2, 4) and Q( – 3, — 1, 5). - r(t)…

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Q: Find a plane containing the point (6, 8, – 8) and the line r(t) = ( − 2, 6, 7) + t - 5, 3, − 3).

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