Consider the function f(x) = sin pi x + 5x - 8. Carefully show that f has an inv
ID: 2862531 • Letter: C
Question
Consider the function f(x) = sin pi x + 5x - 8. Carefully show that f has an inverse function g(x). Find g'(-3) = (f^-1)(-3). Find lim_x rightarrow 0 ?(x + e^x/2)^1/pi. [An answer from the calculator is not enough.] Find the solution of the differential equation dy/dx = e^x/2 squareroot 9 + y^2/y that satisfies the initial condition y(0) = 4. Set up the integral which represents the arc length of the hyperbola xy = 1 from x = 1 to x = 10. Use your calculator to evaluate the integral in part (a) to 2 decimal places. Let R be the region in the first quadrant bounded by the curves y = x^2 and y^2 = 8x. Sketch R and find its area. Find the volume generated by rotating R about the x - axis using the disk-washer method the method of cylindrical shells. Find the radius and interval of convergence for the power seriesExplanation / Answer
3)f(x)=sin(pi x)+5x -8
a) f(a)=f(b)
sin(pi a)+5a -8=sin(pi b)+5b -8
sin(pi a)+5a =sin(pi b)+5b
equating respectiveterms
a=b
so function is one to one
so function has inverse g(x)
b)f(x)=sin(pi x)+5x -8
f(1)=sin(pi )+5 -8
f(1)=-3
f-1(-3)=1
g'(-3)
=(f-1)'(-3)
=1/f '(f-1(-3))
=1/f '(1)
f(x)=sin(pi x)+5x -8
f '(x)=(pi)cos(pi x)+5
f '(1)=(pi)cos(pi ) +5
f '(1)=5-pi
g'(-3) =1/f '(1) =1/(5-pi)