1. For what values of a would the lim x→a sin(x)/x be indeterminate? How could you find the limit at this value? 2. Is it possible for a function with a domain of all real numbers to have a point or points of discontinuity?

3. Discuss the relationship between the continuity of a function at point a and the left-hand derivative (LHD) and right-hand derivative (RHD) at point a.

your limit involves trigonometric terms, such as sine or cosine, try to replace parts of the function with alternative forms of the terms if direct substitution gives you an indeterminate form. For example, if your function is f(x) = (1 - cos²x)/(sinx), you could replace 1 - cos²x with sin²x (as sin²x + cos²x = 1) and then cancel the sinx in the denominator, leaving you with f(x) = sinx.

100%(8)

Step-by-step explanation:

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.