Econ 1530 assignment
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Econ 1530 assignment
- In each of the following equations, suppose g is a given differentiable function of one variable. Suppose the equation defines y implicitly as a function of x. Find an expression for y in each case. (a)xy=g(x) +y^3 (b)g(x+y) =x^2 +y^2 (c) (xy+ 1)^2 =g(x^2 y)
- Suppose the function f is defined for all real x by the following formula: f(x) =x^5 + 3x^3 + 6×3. Show that f has an inverse function g, and then, given that f(1)=7, find g(7).
- Find the linear approximation to the following functions about x=0: (a)f(x) = (1 +x)^1 (b)f(x) = (1 +x)^5 (c)f(x) = (1x)^1 /^4
- Determine the values of x at which each of the functions defined by the following formulas is continuous: (a)x 2 x+1 (b)x
(^8) 3 x (^2) + x^2 +2x 2 (c) ^1 x+ x^7 (x+2)^3 /^2
- Use LHopital rule to find the following Limits:
(a) limx 1 ln(xx1)x+1 2 (b) limx (^1) x^11 ln^74 xx+1+4 (c) limx 1 x xx 1 x+lnx
- Find the intervals where the following functions are increasing: (a)y= (lnx)^2 4 (b)y= ln (ex+ex) (c)y=x^32 ln (x^2 + 2)
- What is the present value of 15 annual deposits of$3500 if the first deposit is after one year and the annual interest rate is 12%?