Greatest integer function Find (a)
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University Calculus
- lim f(x) x--> 3, where f(x) = {2(x+1), if x < 3 or 4, if x = 3, or x^2 - 1, if x > 3} piecewise.they have the limit as 8? why?arrow_forwardSketch the graph of the function defined piecewise by the formulaf(x) = {0, x ≤ −1 ; √1 − x^2 , −1 < x < 1 , x, x ≥ 1 ) A positive number _ and the limit L of a function f at a are given. Find a number δ such that|f(x) − L| < _ if 0 < |x − a| < δ. limx→3 x^2−9/x−3= 6; ϵ = 0.05arrow_forward1. Evaluate the limit algebraically if they exist. The limit as of x approaches 3, square root of x minus the square root of 3 divided by x minus 3.arrow_forward
- a. What is the domain of f? Express your answer in interval notation. f(x)= 1 - x^4 / x^2 - 1 b. Use a sequence of values of x near a=1 to estimate the value of limx→1 f(x). The sequence should include values such as 1.01, 1.001, etc. c. Use algebra to simplify the expression 1 - x^4 / x^2 - 1 d. True or false: f(1)=-2 e. Based on all of your work above, construct an accurate, labeled graph of y=f(x) on the interval [0,2].arrow_forwardUse properties of limits and algebraic methods to find the limit, if it exists. lim x→−3 x2 − 9 x + 3 Step 1 We want to use properties of limits and algebraic methods to find lim x→−3 x2 − 9 x + 3 . Note that the function is a function. The numerator and denominator are 0 at x = , and thus we have the indeterminate form at x = . We can factor from the numerator and reduce the fraction. lim x→−3 x2 − 9 x + 3 = lim x→−3 (x − 3) x + 3 = lim x→−3 = − 3 =arrow_forwardfind the limit L. Then using the Epsilon-delta definition to prove that the limit is L. lim x-> -4 (x2+4x) can you show the formula and show steps to get the answerarrow_forward
- 1-How to find a Limit Numerically (using a chart or table) 2-How to find a Limit Analytically (using a sketch or graph) 3-How to find a Limit Analytically (using algebra techniques)arrow_forwardIf lim f(x) =5 x-->1- and lim f(x)=5 x-->1+, what can you say about lim f(x) x-->1? What can you say about f(1)?arrow_forwardWhat rational function satisfies these conditions? lim f(x)=10 (x-->3), lim f(x) =2 (x---> infinity) lim f(x) =2 (x --> -infinity), f(0) =2arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage