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- Finding a Limit In Exercises 41-46, write a simpler function that agrees with the given function at all but one point. Then find the limit of the function. Use a graphing utility to confirm your result. limx→0 x2 − 5x2/x2-t+2 Evaluate the lim (-2)Solve the problem. lim The cost of manufacturing a particular videotape is c(x) = 10,000+ 12x, where x is the number of tapes produced. The average cost per tape, denoted by , is found by dividing cx) by x. Find *-2,000 (x). O 24 10 A O 17 O Does not exist
- Distance A line with slope m passes through the point (0, – 2). (a) Write the distance d between the line and the point (4, 2) as a function of m. (Hint: See Section P.2, Exercise 77.) (b) Use a graphing utility to graph the equation in part (a). (c) Find lim d(m) and lim d(m). Interpret the results geometrically.Q 3/ A- Find lim,3r+x-5 (1) Find lim 1. 1-2x-x
- f(c+Ax)-f(c) The expression lim Ax→0 is important in the study of calculus. Match the parts of Ax this expression with their meanings in context of the graph. C+Ax 1. The y-coordinate of point P. 2. The y-coordinate of point Q. 3. The horizontal distance from point P to point Q. f(c+Ax)-f(c) Ax lim Ax→0 f(c+Ax)=f(c) Ax 4. The vertical distance from point P to point Q. f(c + Ax) 5. The straight-line distance from P to Q. f(c + Ax) – f(c) 6. The slope of the secant line joining P and Q. 7. The slope of the tangent line at P. 8. The slope of the tangent line at Q.f(4+h)-f(4) Find lim if f(x) =x2 + 4. h>0 f(4 +h)-f(4) lim (Simplify your answer.) 0+-4Tutorial Exercise Use the given graph of the function y = f(x) to find the following quantities, if they exist. y 3 1 -6 -5 -4 -3 -2 -1 1 (a) lim f(x) X-4 (b) lim f(x) X-1- (c) x--1+ lim f(x) (d) lim f(x) x--1 (e) f(-1) Step 1 of 3 (a) lim f(x) X→-4 Recall lim f(x) exists if and only if lim f(x) = lim f(x). a+ Xa Xa Also recall lim f(x) = L if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a for Xa x a. Using the graph, find the values (if they exist) of lim f(x) and lim f(x). (If a limit does not exist, enter DNE.) X→-4+ X-4- lim f(x) = X→-4- lim f(x) = X→-4+ O, lim f(x) ---Select--- X--4 O and its value is as follows. (If the limit does not Since these limits -Select--- exist, enter DNE.) lim f(x) = X-4