Consider the function 1– cos(x) f(x): (a) (T) Evaluate lim, →0 f(x) = L. (b) (T) As x → 0, at what rate does f(x) → L? (c) Compute f(x) as written on a computer for values of x = 10-1, 1o-2, …, 10–10. Com- ment on your results. (d) Suppose that we are able to represent floating point numbers with N decimal digits of accuracy. Around what value of r will the evaluation of f(x) produce very large relative errors when |x| < r? (e) Rearrange the expression for f(x) to a mathematically equivalent expression so that the this new function evaluates accurately for very small values of x. Verify the success of your rearrangement computationally. Are there values of x where you expect accuracy problems with your rearrangement?

Q: 8. Give the equation of the tangent line to the graph of the function f(x)=x√√/25 - x² in the point…

A:

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A: If    limx→cf(x)-f(c)x-c  exists;

Q: lim X→0 1 - cos 8x (e³x-1)²

A: Limx-0-1]2

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A: Given  The function are  1) fx=3x2-10x+6 5) fx=8x    Formula :- f'(x)=limh→0fx+h-fxh .

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A: The given function is ; f(x)=x2-3x.

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A: Both question are solved as, follow

Q: Bruce and Cruz had 294 bookmarks altogether. Bruce gave away 3/8 of his bookmarks and Cruz gave away…

A: Let the number of bookmarks Bruce has = B The number of bookmarks Cruz has = C therefore B+C=294…

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A: We have to find limit

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Q: -5 -4 -3 -2 -1 3 -1 У 1 2 3

A: Limit of the function

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.