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- Use the graphs (see images for said graphs) and the limit laws to evaluate limx -> -3+ f(x) + g(x)Complete (a) and (b). You can verify your conclusions by graphing the functions with a graphing calculator. lim x→∞ 6/x + 9 (a) Use analytic methods to evaluate the limit. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.)Complete (a) and (b). You can verify your conclusions by graphing the functions with a graphing calculator. lim x→−∞ 3x^3 − 4x/9x^3 − 2 (a) Use analytic methods to evaluate the limit. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.)
- Determine the value of the following limit, if it exists. If infinite, specify either infinity or -infinity. (If an answer does not exist, enter DNE.) View picture below for better clarity. lim x → 2 (x+1-squareroot(x^2+3x-1)) / (6-3x) =?Find the limits. Write ∞ or -∞ where appropriate. lim(x/2 - 1/x)as x→ 0+Evaluate the limit lim y approaches 5 1/y-1/5 divide by y-5
- Evaluate the limit numerically or state that the limit does not exist. (Round your answer to three decimal places. If you need to use or –, enter INFINITY or –INFINITY, respectively. If an answer does not exist, enter DNE.) lim x → 7+ x-8 x2-49Determine if the following limit exists. If it does exist, compute the limit. limx→0 x3+7x/x Select the correct choice below and fill in any answer boxes in your choice. A. limx→0 x 3+7x/x=nothing (Simplify your answer.) B. The limit does not exist.Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.) lim h→0 7(x + h)2 − 7x2 h
- Tell whether each statement is true or false. If the statement is true, write TRUE on the space provided before each item, otherwise, write FALSE and change the underlined word to make the statement true. 1. If lim?→3 ?(?)=?, then ?=?(3). 2. One-sided limits work like regular two-sided limits except that ? approaches ? from just the left or just the right. 3. The limit of a function does not exist if the left-hand and right-hand limits are equal. 4. Direct substitution can be directly applied to evaluate lim?→1 1?+1 − 12 ?−1. 5. If the line ?=1 is a vertical asymptote of ?=?(?), then ? is not defined at 1.Evaluate the limit and express your answer in simplest form. \lim_{h\rightarrow 0}\frac{\arctan \left(\frac{1}{4}+h\right)-\arctan \left(\frac{1}{4}\right)}{h}h→0limharctan(41+h)−arctan(41)Estimate the limit numerically if it exists. HINT [See Examples 1-3.] (If you need to use or –, enter INFINITY or –INFINITY, respectively. If an answer does not exist, enter DNE.) lim x→0 x − 3 x − 3