Identifying definite
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- Determine whether f is differentiable at x=0 by considering limh→0f(0+h)−f(0) / h. f(x)=7−x Choose the correct answer below. A. The function f is differentiable at x=0 because both the left- and right-hand limits of the difference quotient exist at x=0. B. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient do not exist at x=0. C. The function f is differentiable at x=0 because the graph has a sharp corner at x=0. D. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient exist at x=0, but are not equal.arrow_forwardThis exercise and the next explore partial converses of the Continuous Limit Theorem (Theorem 6.2.6). Assume fn → f pointwise on [a, b] and the limit function f is continuous on [a, b]. If each fn is increasing (but not necessarily continuous), show fn → f uniformly.arrow_forwardDetermine whether f is differentiable at x=0 by considering limh→0f(0+h)−f(0)h. f(x)=18−x Choose the correct answer below. A. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient do not exist at x=0. B. The function f is not differentiable at x=0 because the left- and right-hand limits of the difference quotient exist at x=0, but are not equal. C. The function f is differentiable at x=0 because the graph has a sharp corner at x=0. D. The function f is differentiable at x=0 because both the left- and right-hand limits of the difference quotient exist at x=0.arrow_forward
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- 5)Use the definition of continuity and limit value (the “-δ definition”) to display the following:Let f: R → R be a function that is continuous in x = 0, and that has the propertythat if x ≠ 0 then f (x) is ≥ 0. Then f (0) is ≥ 0.(Note that it is only assumed that f is continuous in point a, not in an area of a.)arrow_forward5) explain and use the definition of continuity and limit value (the “-δ definition”) to display the following:Let f: R → R be a function that is continuous in x = 0, and that has the propertythat if x ≠ 0 then f (x) is ≥ 0. Then f (0) is ≥ 0.(Note that it is only assumed that f is continuous in point a, not in an area of a.)arrow_forward(a) Express the area under the curve y =x5 from 0 to 2 asa limit.(b) Use a computer algebra system to find the sum in yourexpression from part (a).(c) Evaluate the limit in part (a).arrow_forward
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