In Problems 66–67, find a value of the constant k such that the limit exists.

Suppose that we define the function f as follows: f(x) = √2x + 5 whenever x is not equal to 10 and f(10) = 20. It is clear that the limit of f(x), as x approaches 10, is 5. Let = 0.01. In other words, in this problem we are given that epsilon is 0.01. Find the maximum allowable numerical value of d that satisfies the following: If x is in the interval (10-d, 10+d) and x is not equal to 10, then f(x) will be in the interval (5-0.01, 5 +0.01). Type the exact answer as a decimal in the answer box below. The maximum allowable numerical value for d is:

In a bag of 340 chocolate candies, 35 of them are brown. The candy company claims that 13% of its plain chocolate candies are brown. For the following, assume that the claim of 13% is true, and assume that a sample consists of 340 chocolate candies. Complete parts (a) through (e) below a. For the 340 chocolate candies, use the range rule of thumb to identify the limits separating numbers of brown chocolate candies that are significantly low and those that are significantly high.Values of brown candies or fewer are significantly low. (Round to one decimal place as needed.)

2 Problem 1: (a) State the definition of a limit, e.g., define what it means for limc f(x) = L (b) Provide an e-o proof of lim+1 x +3x = 4. If true nrovide a o ar falco