Determine the rate of change of the function g(x, y) = y² tan(x − 2y + 4) 2) in the direction of the vector = 21 – 2ĵ. at the point (2)

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A: To find: The domain of the function: f(x)=log4(4-3x)

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A: We can find the answer as below.

Q: Identify and sketch the domain of f(x, y) = √4-x²-y In x

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Q: Find the partial fraction decomposition of 12x³ - 37x² +48x - 36 (x - 2)² (x²+4)

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A: Information                                             Graphical interpretation

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Q: B) Find the area of the region between the curves x = quardrant. = y² and x = y + 2 in the first

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Q: Evaluate the following limits. If needed, enter oo for oo and -oo for -0. (a) lim (-37x² + 192³) =…

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Q: 1 — A [1-2 - 2 -5 1+4

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Q: ind a value of h for which 3.0 2.5 h = o in y 2.0 1.5 1.0+ 0.5 f(2+h)-f(2) h 0.5 1.0 Give your…

A: Given Graph:-

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Q: 3- 2 01 -8-7-1 T 2 -3- # Determine which one of the following rules for continuity is first violated…

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A: Finding the derivative using the definition

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A: all six are solved

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Q: 2. Find lim (3x° + V9x6 − 2x3) 第→○ 2

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A: Topic = Limits

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Q: - 8(x,y) = { -5x²y³ 3x4+7y6 if (x, y) = (0, if (x )

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A: To show that the function fx=x-2 is not differentiable at 2.To find a formula for f' and to sketch…

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A: To find out that the limit of the given function at x=0 exist or not.

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Q: 3. Consider f(x) defined as follows: f(x) = 5x² + 13x + 6 |x + 2| [4 - 3x] + x, " x-2 Determine if…

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Q: Does it mean that the limit of the function 2y + [[2-y]] / y^2 + y -2 as x approaches -2 from the…

A: limx→a+f(x) represents the Right hand limit )L.H.L)and  limx→a-f(x) represents the Left Hand limit…

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Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

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Q: 7. Assume that f is continuous and differentiable on (-xx, o0). Consider the interval (a, b) where a…

A: Concept Used: Extreme value theorem: A function must possess a maximum and a minimum if it is…

Q: Prove that (x₁, y₁), (x2, y₂), and (x3, Y3) are collinear points if and only if X1 Y1 1 2 Y2 3 y3 1…

A: The given points are:   x1, y1,  x2, y2  and  x3, y3

Q: 3. Consider f(x) defined as follows: f(x) = 5x² + 13x + 6 |x + 2| [4 - 3x] + x, " x<-2 x ≥ −2…

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Q: 3. f(x) = tan(sin x²)

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Q: By differentation rules, evaluate the derivative of this and simplify as possible.

A: Given, y=x2+42x

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Q: dentify and sketch the domain of f(x, y) = √x-y In (1 + y - x²)

A: solution is given below

Q: The graph below is the function f(x) -5-4-3-2 Find lim * 2- Find lim * 2+ 3 Find f(2) -2 -3 -5+ =…

A: Topic = Limits

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A: The graph of f(x) is given in question and we want to find the right hand limit of f(x) ar x= -2

Q: [1 2 4] A = 3 3 1 6 k 32

A: Given :A=124316k32Matrix is invertible