Concept explainers
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
If g(x) = x5, then
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Single Variable Calculus: Early Transcendentals
- the graph of f(x) is shown f(x)=(x^(2)+2x-3)/(x^(2)+4x-5) what is the limt of \lim_(x->\infty )f(x)? A; -5 B, 0 C, 1 D, \inftyarrow_forwardf(x)=xe^-x How can you use limits to decide which of the two factor functions in f(x) dominates as x approachesinfinity? Can you explain it by writing it in setence and show the matharrow_forwardP(x)=92x-x^2-1760 find limx->40 P(x)arrow_forward
- limx→2f(x)arrow_forwardLet (x) = |x - 2| / x - 2 A) what is the domain of g(x)? B) Use numerical methods to find lim x—> 2- g(x) and lim x—> 2+ g(x). C) based on your answer to (b), what is lim x—> 2 g(x)? D) sketch an accurate graph of g(x) on the interval [-4,4]. Be sure to include any needed open or closed circles.arrow_forwardlimx→∞ f(x) = ∞ and limx→∞ (g(x) − xf(x)) = 2021.If possible, determinelimx→∞ f(x)/g(x).arrow_forward
- determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 exists, then lim x→7 f(x) = 0. True. If lim x→7 f(x) is not equal to zero and lim x→7 g(x) = 0, then lim x→7 f(x)/g(x) does not exist. True. Any number divided by zero is equal to zero. False. Let g(x) = (x − 7) and f(x) = (x − 1)(x − 7). Then lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 exists, but lim x→7 f(x) is not equal to 0. False. Divison by zero is not allowed. False. There is not enough information given to determine lim x→7 f(x)/g(x)arrow_forwardFind lim x3 + 3x2 + 3x + 1 x - 1 2x3 + 3x2 - 1 Find the values of A, so that the function F (x) = {1-3x x <4 Ax2 + 2x - 3 x > 4 is continous for all values of x Thanksarrow_forwardTrue or False? b). If lim x -> 5f(x) = DNE, then f (5) =DNE.If the statement is TRUE, explain why. If the statement is FALSE, sketch the graph of a counterexample.arrow_forward
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