c. Let x/3 and note that as x0.-0. Use lim n sin t to show that L+ 9 27 d. Solve

Question

c. Let x/3 and note that as x0.-0. Use lim n sin t to show that L+ 9 27 d. Solve for L and check for agreement with part (a). Source: Teaching Mathematics and its Applications, Fabio Cavallini, 3, 1988). 55. Two methods The derivative of a function f at a point a is given by a. 3h-1 . Find a possible f and a, and evaluate the limit. im 3h1 b. Evaluate limusing 1'Hôpital's Rule. h--+0 56. Two Methods a. The derivative of a function f at a point a is given by et1 lim x?0 . Find a possible f and a, and evaluate the limit. x b. Evaluate lim x-0x using l'Hôpital's Rule. lin et plications Compound interest Suppose you make a deposit of SP into a savings account that earns interest at a rate of 100r % per yea a. Show that if interest is compounded once per year, then th balance after t years is B(t) P(1 + r)'. b. If interest is compounded m times per year, then the bala after t years is B(t) P(1 + r/m"t. For example, m corresponds to monthly compounding, and the interest ra o the compoundi

Explanation / Answer

By using l hospital rule we can easily find the limit of this function because it is in the (0/0) form.

We have to differentiate the upper and lower function.

3^h.ln(3) and put h = 0 then

Value of limit will be = ln(3).... answer

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