Determine where the function discontinuous. [-(x+2)² +1→x≤-2 f(x)=x+1→-2≤x≤3 [(x-3)² −1→x>3 Using this information and using calculus methods only, show all your work.

Q: If we know that g is a derivable function such that g'(81) = 6 and f is a function given by f(x) =…

A: Given :f(x)=gx4g'(81)=6

Q: If g(x, y) = x² + y² 6x, find the gradient vector Vg(1, 6). Vg(1, 6) = -4,12 Use the gradient vector…

A: Given that , gx,y=x2+y2-6x find the gradient vector ∇g1,6 and tangent line to the level curve…

Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

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Q: Solve using Inverse Operaators. y"" - y' = 4e-x + 3e2x; Particular Solution: Y=C₁+ C₂ eax + C3 ebx…

A: See the details solution in below

Q: c. Given f(x) = 2x - 3, g(x) = -4x² + 9, h(x) = 4x² - 12x +9; find 1. f(x)* g(x) 2. h(x)/ f(x) 3.…

A: solve

Q: (3x²-1) 5x3-5x+13 - dx equals In 15x³5x + 13| + c In 15x³ - 5x + c 5 O 1 In 15x³ - 5x + 13| + c 5 In…

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Q: Use Euler's method with step size 0.1 to estimate y(0.4), where y(x) is the solution of the…

A: To solve the initial value problem.

Q: Let one week's supply and demand functions for gasoline be given by p= D(q) = 288-39 and p = S(q) =…

A: Here, the demand and supply functions are: D(q)=288-43q & S(q)=23q which are the linear…

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i-3j-k, find vector normal to A and In plane of A and, B.

A: See the details solution in below

Q: 5. Calculate the area between the Curve fex) = 4-x² and y = 4, y = 2x_4? 20 GMS: S-U 3

A: To find the area bounded by the curves f(x)=4-x2, y=4, y=2x-4. The region bounded by the curves is:

Q: Using the Inverse Function Theorem, what is (-) (8) given that f(x)=√6x-2? Note that (11) = 8. (B8…

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Q: Question 10 Given z = (e-22) (sin y), find 92 O-2e-2 O-2 e 2 (sin y) + e-2 (cos y) O-2e-2 (sin y) -2…

A: We have to find derivative of given term.

Q: Given f(x) = 3-5x³, use a table to estimate the slope of the tangent line to f at the point P(0, 3).…

A: According to question,Given Function,fx = 3-5x3P0, 3Qx, fx

Q: Find the first and second derivatives of the function: f(x)=(-3x+3)(-2x+1) Simplify your answers.…

A: We have to find out derivative

Q: ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated…

A: You have asked question (2) According to question,Given Matrix,A = 3006-306-63Eigen Values = 3, -3

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: Classroom activity 9.1 the monthly income earned by each of the following workers paid by the hour…

A: We have to determine the monthly income.

Q: a. Determine whether the Mean Value Theorem applies to the function f(x)=ex on the given interval…

A: The given function f(x)=ex on the interval 0, ln 9

Q: QUESTION 5 Given function f(x,y)= A. 2 B. 3 C. D. 0 ANSWER: 6 2 63xy of Evaluate at point (0, 1). ox

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Q: which f(x) is negative. Determine the intervals on which f(x) is positive and on…

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Q: Proceed as in this example to find the solution of the given initial-value problem. Evaluate the…

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Q: Concept Check: Evaluate the following integrals: 1. f(3u³ - 2u³ +/u) du

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Q: On which of the following interval is f(x) = O (0, +∞) O [2, +∞) O (2, +∞0) 1 x-2 continuous?

A: Given: Graph:

Q: Suppose that the total profit function for a company is given by P(x) = 4x³ — 210x² + 3600x - 200,…

A:

Q: Determine dy/dx given that y = 1+sin x COS C 1 O (1+sin x)² -1 O 1+sin x 1 O 1+sin x -1 O (1+sin x)²

A: The objective of the question is determine the derivative of the given function and choose the…

Q: Write the logarithmic equation y = log5x² in exponential form.

A: We are authorised to solve only one question please repost remaining questions Logarithm

Q: Q2A)Matrix 4 = [],find Eigen values of 4². A

A: The given matrix is  A= 1342. We have to find eigenvalues of A2. Eigenvalues are the roots of the…

Q: 16. Using the Quotient tanx= sinx/cosx to prove d/dx tanx=sec2x

A: Quotient rule of differentiation

Q: Q2A)Matrix 4 = [3] find Eigen values of 4².

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Q: 2. Evaluate 6x²e4x³ dx.

A: Let 4x3 = t

Q: Given f(x) = -7x - 2, find f' (5) using the definition of a derivative. Provide your answer below:…

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Q: SSF-n de of F-xy 1-2 k outward (normal away from the z-axis) through the cone z-6√ Use a…

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Q: Q4A)Find area bounded by y = 0, y =√x-x² using double integration.

A: In this question, we want to find the area bounded by the given curves.

Q: Evaluate the following integral. 48x² S dx (x-15)(x+5)²

A: Solution of given question is written in below steps.

Q: B. Given that f(x) = {(-2,1), (1,4), (2,5), (3,6)} g(x) = 6 + 4x h(x) = -x² + 2 find 2.…

A: According to question,Given Function,fx = -2, 1, 1, 4, 2, 5, 3, 6gx = 6+4xhx = -x2 + 2

Q: The position function of an object is given by s(t) = 2³-12² + 30t+8, where time, t, is in seconds…

A: The position function of object is given as  s(t) = 2t3-12t2+30t+8  Where 't' time in seconds and…

Q: Find the average value f of the function f on the given interval. ave f(x) = 6x - x², [0, 2]

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Q: Evaluate the definite integral. 2 X dx 1 + 4x 0

A: Take (1+4x)1/2 = t

Q: 3 X and f'(-2) if f(x) = 6x. 8 (-2)=(Simplify your answer. Type

A: Given: f(x)=x38-6xTo find:f'(-2)

Q: Find (s-¹1)' (5) using the Inverse Function Theorem, given that s(x) = −6x³ – 8x² – 9x - 2. Note…

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Q: 5 Find the coefficient of the given term when the expression is expanded by the binomial theorem. x6…

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Q: lim x²+3x sin x x-0 0 3 01 O does not exist 0 0

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Q: The demand function for a product is given by P(x) = 80 -0.018x, where x is the number of units of…

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Q: calculate the lengths of all three sides using the distance formula of the non-right angle triangle…

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Q: dx dt 4x + y dy x + 2y dt a) Find the general solution for x(t) and y(t) b) Solve the initial value…

A: Given that,

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A:

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B.…

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Q: Given that f(x) = (x - 6)² and g(x) = 1 and g(x) = 1 – 2x, find

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Q: Find the scalar and vector projections of b onto a. a = (1,6), b = (-7, 1) compab = projb =

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Q: dx 17 +2ox +5х2

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…