Calculus Quiz

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your answers and work in this copy of the quiz, or if you prefer, create a document containing your work. attach is the week 1 Calculus Quiz to be completed before June 28Quiz-1, Math 140(40%) True or False__ __ if x→c- f(x) = x→c+ f(x), then f is continuous at x=c. _______ If f(x)=[x] is an integer function (see 0.4) then f(x)-f(x-0.00001)=1, when x-1.     _  __If the , then does not exist.______ For any statement A and B, if A implies B, then B always implies A. _______ The limit does not exist because the function, f(x)= , is not defined at x=2. _____ If x→c f(x) =L, and f is continuous, then L=f(c). _____ If , then ____ If f(x) is always bounded between the two functions, h(x)=x2+2, and g(x)=2x +1, then x→1 f(x) =3._ ___ If x→c f(x)g(x) exists then both x→c f(x) and x→c g(x) exists, regardless of the conditions of individual functions. __ __ If x→c f(x) =L then L=f(c) __  __ If f is continuous at x=a, then the tangent at x=a exists.            if f is a function and f(a) = f(b) then a = b. ______ If f is continuous at x=c, then x→c- f(x) = x→c+ f(x)           If f is discontinuous at x=a then x→af(x) does not exit.             If f is a continuous function and f(x1) and f(x2) have opposite signs, then the function f has a root in the interval (x1, x2).             It is possible to find an exact area under the graph f(x)=1/x, bounded by x=0 and x=1.             You can always use bisection algorithm to find a root of a continuous function. ___ __ If a continuous function f(x) has a root at x=a, then there always exists a number ε such that f(a- ε) and f(a+ ε) have opposite sign. ______If f(x) is continuous at x=a, then a slope exists at x=a.  ______ If f is continuous at x=c, then . (You must show your work to get full credit for the problems below)(15%) Consider the statement A: “If a creature is a human, it has 2 legs”. (1) What is the converse of A? (2) What is the contrapositive of A? (3) Which one, (1), or (2), above is always true: (15%) Does a tangent line exist everywhere for the function ?    Explain your conclusion.(15%) Use the bisection method to find at least one value of x such that   cos(x) = x.  The solution should be within accuracy of 0.05.  That is, if the actual answer is “r”, then a solution “s” satisfying the condition if |s-r| <0.05. (15%) Find the 1- and 2-sided limits of the function, f, as x approaches 0, 1, and 2, where . (Note: Since x is a real number, x in sin(x) is a radian)

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