5. Suppose that f: R→ R is continuous. and f(x) > 0.. Prove that there is an in- terval I = (10-120+1), where n is natural number, such that f(x) > 0 for all z in I.
5. Suppose that f: R→ R is continuous. and f(x) > 0.. Prove that there is an in- terval I = (10-120+1), where n is natural number, such that f(x) > 0 for all z in I.
5. Suppose that f: R→ R is continuous. and f(x) > 0.. Prove that there is an in- terval I = (10-120+1), where n is natural number, such that f(x) > 0 for all z in I.
Transcribed Image Text:4. Suppose f: [a,b] → R is continuous. Let g = inff. Show that there is a point zo
in [a, b] such that f(zo) = 9 (Hint: Imitate the proof given in the class to show that
any continuous function attains its supremum).)
5. Suppose that f: R→ R is continuous. and f(x) > 0.. Prove that there is an in-
terval I = (20-20+1), where n is natural number, such that f(x) > 0 for all z in I.
More advanced version of multivariable calculus. Advanced calculus includes multivariable limits, partial derivatives, inverse and implicit function theorems, double and triple integrals, vector calculus, divergence theorem and stokes theorem, advanced series, and power series.
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![4. Suppose f: [a,b] → R is continuous. Let g = inff. Show that there is a point zo
in [a, b] such that f(zo) = 9 (Hint: Imitate the proof given in the class to show that
any continuous function attains its supremum).)
5. Suppose that f: R→ R is continuous. and f(x) > 0.. Prove that there is an in-
terval I = (20-20+1), where n is natural number, such that f(x) > 0 for all z in I.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30e714d6-c3d6-4fe9-9c10-b4b8c64f125f%2Faeb754b4-caf5-480b-a9ce-7816d114aa7f%2Fgaw08r_processed.jpeg&w=3840&q=75)
