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In Problems 15-40, use properties of limits and algebraic methods to find the limits, if they exist.
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- The graph below is the function f(x) -4 -1 lim x-2+ 5- 4 3 2 + Determine the following values. Enter "DNE" if a value does not exist, enter "oo" (lower case "o") if the limit approaches positive infinity, or "-oo" if the limit approaches negative infinity. f(-2) + lim f(x) = x-2- lim f(x) x--2 -2 f(x) =arrow_forward2. To evaluate the limit of a function, we often need to first rewrite the function using the rules of algebra. What is the logical first step in evaluating each of the following limits? (5 + h)? – 25 (a) lim 2 x - 2 (b) lim h Vx +I- 2 .7 (d) lim 7 x- 7 (c) lim x- 3arrow_forwardSuppose a state's income tax code states that tax liability is 18% on the first $19,500 of taxable earning and 14% on the remainder. Find constants a and b for the tax function 7(x) - Ja + 0.18x [b+0.14(x-19,500) x 19,500 x> 19,500 such that lim T(x) = 0 and 40 a0 b lim x-19,500 7(x) exists.arrow_forward
- Find the limitarrow_forwardConsider the follovwing graph of the function g. From the given graph of g, state the numbers at which g is discontinuous. (Enter your answers as a comma-separated list.)arrow_forwardTrue or False The limit of a function is defined when at x=a, f(a) is a real number. The function assumes an indeterminate form when x=a, both the numerator and denominator approaches zero. The expression y2 = 5x+4 is a function.arrow_forward
- 3x + 5; if xs1 1- 2x + b;if x>1 b) The function f(x) is defined by f(x) = { , If lim f(x)exists, what is the value of b?arrow_forward2x а. lim x-3 X- 3arrow_forwardThe graph below is the function f (x) -5 -4 -3 -2 -1 +-+ -3 -4 -S lim f(x) = x-3- lim f(x) = x-3 f(3) = lim f(x) = x 3+ 5 4 3 2 + Determine the following values. Enter "DNE" if a value does not exist, enter "oo" (lower case "o") if the limit approaches positive infinity, or "-oo" if the limit approaches negative infinity. Ā 2. Determine if the function is continuous or discontinuous at the limit value. If it is discontinuous, indicate if the discontinuity is removable or non-removable. O The function is continuous at x = 3 O The function has a removable discontinuity at x = 3 O The function has a non-removable discontinuity at x = 3 If the function has a discontinuity at the limit value, check all the boxes that indicate why the function is discontinuous there.arrow_forward
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell