4. Determine whether the functions f are continuous at given points: x+2 S(x) ={ x +x-2 0, x=1 at x =1 5. S Find lim 4x 0 f(x+Ax)-ƒ(x) if f(x) = Ax

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A: To evaluate the given limits

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Q: 10. Find the value of the limit or state that it does not exist (DNE). a) lim f(x)= =(x)s u X -3

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Q: 6. Use the graph of the function f(x) = He to discuss the limit lim 40 f (x). 1+e!/x

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Q: Compute the limit 1 a2 1 - x2 lim xa x а - What can you say about the derivative of f(x) = ?

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Q: Let f(x) = 3x² – 5x + 1 f(x+h)-f(x) (a) Find f'(x) using the limit definition of derivative. That…

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Q: |Suppose that dy = y3 + y? – 9y – 9 dx %3D and that the point (13, –2) lies on the graph of (x, y).…

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Q: * + 2, if x 0' (a) Find lim f(x). (b) Give a simple reason why f is discontinuous at 0.

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Q: for |x| > 1, 2x2 fx,(x) = 0, %3D otherwise. Let L = lim P(max{X1,..., X,} < n log(v5)). Determine…

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Q: (a) Evaluate the following limit: lim ) (1-e3x x²+3x, x-0 (b) Find the equation of the tangent to…

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Q: x' + 2, if x 0 (a) Find lim f(x).

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Q: -7x2 – 6x + 1 x<0 x 20 f(x) = 3 sin x Enter DNE if the limit does not exist. lim f(x) = 1 lim f(x) =…

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Q: Consider the function - x2, x+1 f(x) = 2, x = 1 O Graph the function f(x). O Find lim,1-f(x) and…

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Q: Find the following limits. √x-3 X-9 x-9 1. lim t²-7t+10 2. lim- t-2 t-2 3. A function f(x) satisfies…

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Q: 1. Show that for all f e L'(R) lim da = 0.

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Q: b. For what value of (k) is the function y=f(x) continuous at x-3. x3-3x2-4x+12 x + 3 x-3 f(x) = %3D…

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