General calc problems

20) If the function f is continuous for all real numbers and lim as h approaches 0 of f(a+h) – f(a)/ h = 7 then which statement is true? a) f(a) = 7 b) f is differentiable at x=a. c) f is differentiable for all real numbers. d) f is increasing for x>0. e) f is increasing for all real differentiable ans is B. Explain ...continues

General calculus

20) If the function f is continuous for all real numbers and lim as h approaches 0 of f(a+h) – f(a)/ h = 7 then which statement is true? a) f(a) = 7 b) f is differentiable at x=a. c) f is differentiable for all real numbers. d) f is increasing for x>0. e) f is increasing for all real differentiable ans is B. Explain ...continues

Calculus

30) If f(x) = ln(sin(x^2)), then f’’(x)=? Explain. 31) The college is making parking lot, rectangular and enclose 6000 sq meters. A fence will surround the lot and on parallel to one of the sides will divide the lot into two sections. What are the dimensions in meters of the rectangle lot using the least amount of fen ...continues

Gen calc

35) Let f be the number of trees in a forest at time t in years. If F is decreasing at a rate given by the equation dF/dt = -2F and if F(0) = 5000, then F(t)= Ans is 5000e^-2t. Explain. 22) Let f be a differentialble function defined on the closed interval [a,b] and let c be a point in the open interval(a,b) such that I ...continues

Rotation Problem for Calc II

a)Find the center of mass with constant density of the region bound by y=x5, y=2-x4 and the y axis; b)Rotate it about the y axis and find its volume; c) Rotate it about the x axis and find its volume.

Differential equation

Given dy/dx= -xy/(ln y), where y>0 find the general solution of the differential equation What solution satisfies the condition that y=e^2 when x=0... express in y=f(x) Why is x=2 not in the domain found from that?

Volume of Ellipsoid

Find the volume of the ellipsoid formed by rotating the semi-ellipse (see attached word file) about the x axis.

Calc II Problem

Find the length of y=cosh x for -1 ¡Ü x ¡Ü 2.

Calc II/Setting up integral to calculate volume of rotation

See attached word file.

Derivatives

Calculate y' (y prime) 1. y = cos(tanx) 2. y = e^(-1)*(t^2-2t+2) 3. y = sin^(-1)*(e^x) 4. y = x^r*e^(sx) 5. y = 1/(sin(x-sinx)) 6. y = ln(csc5x) 7. x^2 cosy + sin2y = xy 8. y = ln(x^2*e^2) 9. y = sec(1+x^2) 10. y = (cosx)^x