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Homework Statement ∫ x sinx cosx dx = Homework Equations note that sinx cosx = (1/2) sin 2x The Attempt at a Solution 1/2) ∫ x sin 2x dx = (1/2) [(-1/2)x cos 2x - ∫ (-1/2)cos 2x dx] = (1/2) [(-1/2)x cos 2x +(1/2) ∫ cos 2x dx] = (-1/4)x cos 2x +(1/4) ∫ cos 2x dx = (-1/4)x cos 2x...

Live cultures of Bacillus thuringiensis (Dipel) and B. subtilis (Kodiak) are sold as pesticides.What bacterial structures make it possible to package and sell these bacteria? For what purpose is each product used? Is it because it's close to anthrax?(endosporish)

Homework Statement Find the integral. (Note: Solve by the simplest method - not all require integration by parts.) ∫t ln(t + 2) dt Homework Equations ∫udv=uv-∫vdu The Attempt at a Solution dv=tdt v=tdt=t2/2 u=ln(t+2) du=1/(t+2)dt ∫t ln(t + 2) dt...

Homework Statement Find Mx,My, & (x bar, y bar) for the laminas of uniform density ρ bounded by the graphs of the equations. (Use rho for ρ as necessary.) x=-y x=5y-y2 Homework Equations m= ∫f(x)-g(x) dx my= ∫x(f(x)-g(x)) dx =>x bar my/m mx= 1/2 ∫ (f(x))2-g(x))2dx => y bar=mx/m...

I got it correct :))

I saw it in an example for the inequality.. The 7 is for the a & b part I don't know how to place the 0 on the bottom.

Homework Statement so I did Homework Equations s=∫ba√(1+[f'(x)]2dx The Attempt at a Solution y=2/3x3/2+7 y'=x1/2 0≤x≤1 =∫6√(1+(x1/2)2)dx =[2/3(1+x)3/2]7 my answer came out wrong

Wow I should have paid close attention the graph is too small haha thank you.

Homework Statement Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. y = √x Homework Equations V=2∏∫p(x)h(x) dx a=0 b=8 The Attempt at a Solution V=2∏∫(x)(√x)dx a=0 b=8...

YAY it finally worked thank you :D

I did this one in my homework online and it keeps saying I'm wrong

okay how about this answer?? f'(x)=arcsec4x+ 4/(4x(√(16x)2-1)

I mean this one (4x)^2

is it 4/(|4x|(√4x2-1)) I keep getting it wrong

Homework Statement find the derivative of the function f(x)=arcsec(4x) Homework Equations I think this is a Relevant equations. d/dx[arcsecu]=u'/(|u|(√u2-1) The Attempt at a Solution f'(x)=4/(|4|(√42-1) =1/√15 I keep getting wrong in my online homework why? :confused:

sorry I just realized that it was for a different problem my answer for this was .805

Homework Statement arctan(8x-8)=-1 Homework Equations I'm sure what this part wants. The Attempt at a Solution tan[arctan(8x-8)]=tan(-1) 8x-8=tan(-1) x=(1/8)(tan(-1)+8) x=(1/8)(-(tan(1)+8) x= I am stuck on the last part since the homework says Simplify the above equation...

f'(x)=1/(1+x2) + -1/(x2+1) =0 for all x≠0 function is constant on domain is this right?

4e2xg'(u) + 2e2xg''(u)

where did that come from I'm confused??

Homework Statement Verify the identity: arctanx + arctan(1/x)=∏/2 using calculus theory. (Hint: Differentiate the left hand side of the identity) Homework Equations ? The Attempt at a Solution is this correct? tan(arctanx + arctan(1/x)) = [tan(arctan(x)) +...

Calculate f" for f(x)=g(e^(2x)), where g is a function defined for all real numbers & g admits second order derivative. please check if I did it right. f = g(e2x) f' = 2e2x g' f'' = 4e2xg' + 2e2xg'' I have expanded out 4e2xg'(u) + 2e2xg''(u)

Yay thanks

Oh I mean √7/√2

Is it (7/2,(√7/2))?

I don't get it?

Yes, I want to check my work if it's correct.

Homework Statement Find the point on the graph of f(x)=√x that is closest to the value (4,0). (differentiate the square of the distance from a point (x,√x) on the graph of f to the point (4,0).) Homework Equations f(x)=√x The Attempt at a Solution Square of distance from (4,0)...

Homework Statement Solve the following differential equation: f"(x)=sinx x(0)=0, x'(0)=1 Homework Equations x(0)=0, x'(0)=1 The Attempt at a Solution f"(x)=sin(x) integrate, f'(x)=-cos(x)+C1 f'(0)=-cos(0)+C1=1 => C1=2 C1=2 f'(x)=-cos(x)+2 f(x)=-sin(x)+2x+C2...

Homework Statement Use logarithmic differentiation to find dy/dx for y=(1+x)^(1/x). Homework Equations dy/dx The Attempt at a Solution ln y = ln (1+x)^(1/x) = (1/x) ln (1+x) (dy/dx) /y = (-1/x^2)(ln(1+x) + (1/x)(1/(1+x) dy/dx = y [(-1/x^2) ( ln(1+x) + x/(1+x) ] or (-1/x^2)(...

What do biophysics do and where do they work?

How much variability exists between the genomes of separate individuals? What is an SNP?

Homework Statement use the elipson-delta of a limit to justify the answer of: show proof lim x->0 1/(x+1) Homework Equations lim x->0 1/(x+1)=1 The Attempt at a Solution lim x->0 1/(x+1) I did some work but after that I don't know how to keep going. if 0<|x-c|<δ =>...

I used a different method.. but that answer sin(sin(0))/0 does not exist right

well in the table for k=2 it goes from -100 then an error then 99 so it must be for all positive numbers and above should be infinity?

I'm not sure.

well I plugged it into my calculator

Homework Statement find the positive integers k for which lim x->0 sin(sin(x))/x^k Homework Equations exists, and then find the value of the limit The Attempt at a Solution I did the first three k's k=0 lim x->0 sin(sin x))/x^0= 0 undefined k=1 lim x->0 sin(sinx))/x^1= 1 k=2 I might be...