Concept explainers
True-False Determine whether the statement is true or false. Explain your answer.
Suppose that
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- true 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_forwardlim f(x) as x approaches infinity lim f(x) as x approaches negative infinityarrow_forwardThe piece-wise function g(θ) is given by g(θ) = { A sec2 θ + 1 : 0 < θ ≤ π/4 {2 tan θ + A : π/4 < θ < π/2 (a) Determine the value of the constant A so that g(θ) is continuous on the interval (0, π/2). (b) Using the value for A from part (a), is g(θ) differentiable on the interval (0, π/2)? Explain your answer.arrow_forward
- lim x to 0 tanh(x)/tan(x) using the L'hospital's rilearrow_forwardLet 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_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage