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H m h fÇ. MATH 140B HW 1 SOLUTIONS Problem1(WR Ch 5 #6) Suppose (a) f is continuous for x ‚0, (b) f 0(x) exists for x ¨0, (c) f (0) ˘0, (d) f 0 is monotonically increasing, Put g(x) ˘ f (x) x (x ¨0)and prove that g is monotonically increasing Solution If we can prove that g0(x) ¨0 for x ¨0, then this will show that g is monotonically increasing (by Theorem 511a) By the quotient rule,. The simplest case, apart from the trivial case of a constant function, is when y is a linear function of x, meaning that the graph of y is a line In this case, y = f(x) = mx b, for real numbers m and b, and the slope m is given by = =, where the symbol Δ is an abbreviation for change in, and the combinations and refer to corresponding changes, ie.

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5 w H s 8 Ò. Funktionerna f(x) = och g(x) = 4 – x 2 och hittar definitionsmängden samt värdemängden för de sammansatta funktiorna Vi måste uppenbarligen begränsa värdet inom kvadratroten till enbart poritiva tal Därför kan sen sammansatta funktionen f(g(x)) = enbart anta positiva värden av den inre funktionen g(x) = 4 – x 2. Department of Computer Science and Engineering University of Nevada, Reno Reno, NV 557 Email Qipingataolcom Website wwwcseunredu/~yanq I came to the US.

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