Concept explainers
Continuity and limits with transcendental functions Determine the interval(s) on which the following functions are continuous; then analyze the given limits.
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Chapter 2 Solutions
Calculus: Early Transcendentals (2nd Edition)
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- 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_forwardThe limit lim x-> 0 e^x-1/x equals a derivative f' (c), for some function f(x) and some real number c. (i) find f(x) and c. (ii) Use the derivative of the function f(x) to evaluate the limit. (iii) Find an equaiton of the tangent line to y = f(x) at x = c, for the value of c you found in (i).arrow_forwardUse L' Hopital's to find the limit as x approaches positive infinity of: (e^(3x))/(x^(2)) I hope you have a nice day!arrow_forward
- looking at the graph of f(x) find the limit as x approaches 0- of f(x)arrow_forwardusing the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x)= 3x2+(x+2)5, a= -1 can you please explain this problem with workarrow_forwardLet f(x)= 2x-2 if x<1 f(x)=x^2-1 if x is greater than or equal to 1 Evaluate Lim h-->0+ f(1+h)-f(1)/h Evaluate Lim h-->0- f(1+h)-f(1)/h Is the function f differentiable at a=1? Justify your answer.arrow_forward
- 5) a function with a domain of (-2, infinity): Consider: Is the function continuous at x=1? If not, what type of discontinuity does the function have at x=1?arrow_forwardlimit as x approaches infinity of (e^x + e^-x)/(e^x - e^-x)arrow_forwardtrue or false questions. please explain why. . 1-if lim_{x->a} f(x)=∞ and y=g(x) is defined and bounded below on an interval containing a , then lim_{x->a} f(x)+g(x)=∞ 2- if 0≤a≤1/e , then the equation x.e^-x=a has a nonnegative solution. 3-suppose that a function y=f(x) is continuous on I=[a,b] and if the set f(I)=[f(a),f(b)], then y=f(x) is strictly increasing.arrow_forward
- True or false: the limit as x approaches infinity of (x^2-x) =0arrow_forwardlimit of (x + 5) as x approaches to 3 po yung given if ever blurred. ty!arrow_forwardGuess 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)=cos(9x)-cos(5x)/x2 We want to find the limit limx→0 cos(9x)−cos(5x)/x2Start 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 cos(9x)−cos(5x)/ x2arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage