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Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Glencoe Math Accelerated, Student Edition
University Calculus: Early Transcendentals (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
- 1. We know that lim as x approaches 0 (sin(x)/x) = 1 a) Explain why this limit statement implies the following approximation: (sin(x)/x) ≈ 1 if x ≈ 0. b) Rearranging this approximation, we get the smalll angle approximation: sin(x) ≈ x if x is small. Test this approximation with some small values of x )use radians). Share the result. Does this approxiamation work? c) Plot both y = sin(x) and y = x on the same axes, and show on the plot how and where the approximation is valid.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_forwardHi I need help on solving this problem for my calculus: Evaluate the limit: lim x -> (3pi)/(2) (sin2(x) + 6 sin(x) + 5)/ (sin2(x) - 1)arrow_forward
- a)Find all values of ?? such that lim x ->a DNE b)Find all the values that f'(x) DNE c)at which of x is f(x) discontinuous what type? d) find lime x->-8 f(x)arrow_forwardFind the limit. Use l'Hospital's Rule if appropriate. I lim x→0 e^x-e^-x-2x/x-sin(x):arrow_forwardlim x to 0 tanh(x)/tan(x) using the L'hospital's rilearrow_forward
- Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x)=e^1.9x−e^3.1x/x. We want to find the limit limx→0 e^1.9x−e^3.1x/x.Start by calculating the values of the function for the inputs listed in this table. x x f(x)f(x) 0.2 0.1 0.05 0.01 0.001 0.0001 0.00001 Based on the values in this table, it appears limx→0 e^1.9x−e^3.1x/x=arrow_forwardlim x -> 0 (3x * cot(3x)) . Do not use sing L'hospitals Rulearrow_forwardThe graph of y=f(x) is given below. Assume limx→−∞ f(x)=3 and end behavior are as indicated on the graph. a) limx→∞ f(5-x) = ? b) limx→∞ (sin(f(x)))/f(x) = ? c) limx→∞ f(x)sin(1/f(x)) = ? d) limx→-1- √(f(x)+5)−√(f(x)+4) = ?arrow_forward
- Let f(x, y) = y sin(1/x). (a) What is the domain of f? I think it's all values of (x,y) where x is not 0 (b) What is the range of f; that is, which values does f(x, y) take for (x, y) in its domain? I think it's all real numbers (c) Determine the limit lim (x,y)→(0,0) y sin(1/x) and explain your answer. (d) For c = 0 and c = 1, write an equation for the level curve f(x, y) = c, and draw them in the region where −2 ≤ x ≤ 2 and −2 ≤ y ≤ 2. Please use two different colors to indicate the two level curves, and feel free to use a graphing calculator to help you! (e) Explain why lim (x,y)→(0,1) y sin(1/x) does not exist. (f) From the surfaces drawn on the back of this page, determine the graph of f. (I attached as an image)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_forwardEvaluate lim t→0 3+t^2 sin(t^3+2/t^2) using limit laws. Give reasons for your answer.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning