04: (chose one only) (3-x x<2 1-f(x) = 2 x = 2 x>2 a) Find lim, 2+ f(x), lim,-2-f(x) andf (2). b) Dose lim, 2 f(x) exist, if so, what is it? If not, why not? c) Dose f(x) is continuous atx = 2.

Q: f(unx) If f (x+ y) = f (x)+ f (y) for all x , y eR and f (1)=1, then evaluate lim - -2/(sinx)…

A: Here the above question can be solved by using basic concepts of limit

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Q: Find f '(a). 3t + 9 f(t) : t + 4 %3D Step 1 To find f'(a), we will use the formula f '(a) = lim t) –…

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Q: If f'is continuous, f(3) = 0, and f '(3) = 6, evaluate f(3 + 5x) + f(3 + 6x) lim

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Q: Use the limit definition of the derivative of the given function at the given value of x (if it…

A: Given functions are

Q: Suppose that in the interval 7 ≤ x ≤ 19 you know that f'(x) is positive and f(x) is negative. Select…

A: Suppose that in the interval  7≤x≤19  you know that f'(x) is positive and f''(x) is negative.

Q: The slope of the tangent line to the graph of the function y = 2x3 at the point (2, 16) is lim2"…

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A: Given query is to find the limit of the expression.

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Q: Use the following information to sketch the graph of a continuous function with the following…

A: The given conditions are : (a) f-3=5, f0=2, f3=0 (b) f'x&gt;0 on -∞,-3∪3,∞and f'x&lt;0 on -3,3…

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Q: x+2a, if x<1 What value for a would makef (x)continuous everywhere? Let f(x)= (ax? +7x-4, if x21

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Q: If limit t y = f(x) write an expression for the differentia dy

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A: Given piecewise function is. fx=x+22, x&lt;-21+x,-2≤x≤4x+42,x&gt;4

Q: find and sketch the range of the function g(x, y) = ln(x ^2+y^2-9)

A: Consider the given equation.g(x,y)=ln(x2+y2-9)   Now, find the domain of the function.x2+y2-9&gt;0…

Q: lim f(x) where f(x) = x→1+ X, x ≤1 1-x, x>1'

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