Differentiate implicitly to find | dx y²-x²=22; (3,-7) ☐ dy . Then find the slope of the curve at the given point. dx The slope of the graph at the given point is (Type an integer or a simplified fraction.)

Q: if f(x, y) is defined at (a, b), then fy(x, y) must also be defined at (a, b)

A: The given  is defined at , then  must also be defined at .The aim is to determine whether the…

Q: f(-2)=3 f'(-2) = 4 g (4) = 5 g (4) = 2 The point (-2,4) lies on the curve in the xy-plane given by…

A: f(-2)=3f'(-2)=4g(4)=5g'(4)=2

Q: Antiderivatives Definition: A function F is an antiderivative of f on an interval I if F'(x) = f(x)…

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Q: Solve each equation for x, where 0≤ x ≤ 2π. ✓ ✓ & ✓ ✓ 3 a) cos²x -2=0 4 b) sin² x - 3 sin x + 2 = 0

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Q: The graph of g(y) = 8 is given below. -6 -5 -4 -3 -2 -1 of & 8 -5 Determine the definite integral…

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Q: Find the inverse of the given matrix, if it exists. Use the algorithm for finding A1 by row reducing…

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Q: 5. a) Simplify the following rational expression. Clearly show all your work! 9-x² 2x² - 7x + 3 te…

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Q: Suppose an investment account is opened with an initial deposit of $13,500 earning 6.75% interest,…

A: Compound continuously formula

Q: Determine an equation in the form ƒ (x) = y-intercept of — 1. ✔✔ 9° 1 kx+c for a function with a…

A: The function is given byVertical asymptote is at y-intercept of the function is

Q: b) Solve the following cubic polynomial equation using the Zero Product Property. Clearly show all…

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Q: For the function f(x) = x² - 6x³ + 1, find the points of inflection. A/

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Q: Solve for the indicated value, and graph the situation showing the solution point. The formula for…

A: The sound intensity in decibels D is defined byandhow many decibels are emitted and draw the graph…

Q: 2-10x+10 -2 perform the division. Express your answer in the Division Algorithm.

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Q: 1 Find the inverse of the given matrix A using Gauss-Jordan elimination. 45 -3 4 -15 55 -164 15 -15…

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Q: The cost (in S) of producing x-units of certain commodity is: C(x)=500+7x+0.03x². Find the average…

A: In this question, we will find the average rate of change and instantaneous rate of change.

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Q: Find the right match for the following ODEs in the dropdown menu = x y y' = 5+ sin(y/x) Choose...…

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Q: 14. The general formula of a sequence is t = 13 2t where t t₁ = 4. Find the fourth n 'n-1' 1 term

A: we are given the general formula of a sequence and we need to find out the fourth term.

Q: Find the derivative G(x)= (x^2+4x-3)e^x

A: To find the derivative of the following function.

Q: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 1300 yd…

A: A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 1300 yd…

Q: Does the following series converge or diverge? Give reasons for your answer. ∞ 6 n!n! Σ (2n)! n=1…

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Q: Devon invested $9500 in three different mutual funds. A fund containing large cap stocks made a 6.8%…

A: Devon invested $9500 in three different mutual funds. A fund containing large cap stocks made a 6.8%…

Q: (1) The critical values of f(x) = 9x4 + 16x³ + 6x² + 7 are at x = (A) 0 only (B) -1 and 0 (C) -1 and…

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Q: b) Fully factor the following polynomial expressions. Clearly show all your steps. -2x²y - 4x³y 6a²…

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Q: (9) Given that g(x) = e(-), which of the following must be true on the interval (0.∞)? (A) f(a) is…

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Q: 5. • lim x-1 • lim x-0 Use the definition of derivative to evaluate the following limits. x²x+1 +x-2…

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Q: View vectors in R as nx1 matrices. For u and v in Rn, the matrix product u v is a 1x1 matrix, called…

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Q: Medical Science Coughing forces the trachea (windpipe) to contract, which in turn affects the…

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Q: gral: 2 [15√² (15√x² - 81 x4 -da stitution is correct for this integral? m(0) (0) (0)

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Q: The population of a small town is modeled by the equation P= 1950e0.5t where t is measured in years.…

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Q: True or false: If f(x) = 12 for all real numbers , then f"(x) = 0 for all real numbers .

A: The question is asking whether the second derivative of a constant function is zero for all real…

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

A: In this question, we will find the sides of the fence.To minimize the cost of the fence, equate the…

Q: A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the…

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Q: Differentiate the function √e-3²+x+1 µ3. f(x)

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Q: Calculate the indicated Riemann sum S3 for the function f(x)=x2−4x−21. Partition ​[0,6​] into…

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Q: For the given function, find the properties listed below. Show work or explain how you got your…

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Q: True or false: O True ● False d dx 1 [2 + ²] = 1 x²

A: The objective of the question is to determine whether the derivative of the function 1/(2 + x^2)…

Q: Find the function f(x) and all values of c such that [F f(t) dt = x² + x - 2. f(x) = C = (Entered as…

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Q: o that the product of one part and the other is

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Q: QUESTION 5 Find the dimensions of the rectangular garden of greatest area that can be fenced off…

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Q: Find the derivative of f (z) = (2²-32-9)" by following these steps. You may assumey-(e) Identify the…

A: The given function is

Q: Find the slope of the tangent line to the polar curve 7 = 1-sin 40 at 0= 04 0- 12/12 O 5√3+4 1-4√3

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Q: True or false: For any constant C, d =[ tan(x) + C] = [sec(x)]² dx

A: The objective of the question is to verify whether the derivative of the function tan(x) + C equals…

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A: By using Newton's law of cooling in the study of heat transfer:-

Q: Hello i need help with this question. Find a cubic function f(x) = ax3 + bx2 + cx + d that has a…

A: The given function  ,the function local maximum value of 2 at x = −2 and a local minimum value of 0…

Q: write a polynomial f(x) that satisfies the given conditions.  Polynomial of lowest degree with…

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Q: Consider the following three vectors in R³: V₁ = If b = , V₂ = 1 0 , V3 = 0 is any vector in R³,…

A: We have to explain why we can always write b as a linear combination of..