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True-False Determine whether the statement is true or false. Explain your answer.
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- a) value of f(1) b) lim x→1-f(x) c) lim x→1+f(x) d) Does lim x→1 f(x) exist? If so, find value. If not, explain why. e) lim x→2+f(x) f) lim x→2-f(x)arrow_forward6. Evaluate lim F(x), where f is defined by F(x) =(picture)arrow_forwardK Explain why lim F(x) in Figure A exists, but lim f(x) in Figure B does not. X→2 X→-2 Figure A AF(x) Since lim F(x) X→2¯ FI in the blanks below. O Since lim f(x) X→-2¯¯ X. lim F(x), lim F(x) X→2* X→2 lim f(x), lim X→-2* X→-2 Loo 4 Figure B Af(x) 2 2 X A Q Q K7arrow_forward
- limx→∞ f(x) = ∞ and limx→∞ (g(x) − xf(x)) = 2021.If possible, determinelimx→∞ f(x)/g(x).arrow_forwardlim x→∞arrow_forwardFigure out that this statement is true or false? if is false explain why? by using example, and if it is true explain why? When lim x → a f ( x ) exists, the limit is always equal to f ( a ) - Is this statement true or false?arrow_forward
- (Question pertaining to indeterminate limits) It is not uncommon for people to write: lim x approaches a f(x) = 0/0 a) Why is this not correct? b) Is 0/0 a number? No. Explain what 0/0 means in terms of the numerator and the denominator.arrow_forwardDifference between f(c) and lim f(x) as x approaches carrow_forwardUsing L'Hospitals Rule, what is limx->infinity (1+3/x)xarrow_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_forwardDetermine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If limxc f(x) = L and f(c) = L, then f is continuous at c.arrow_forwardConsidering the definition of f(x) below, find limx→5−f(x).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage