Recent content by mjstyle

Homework Statement a) Let v be a unit vector in R^3 and u be a vector which is orthogonal to v. Show v x (v x u) = -u b) Let v and u be orthogonal unit vectors in R^3. Show u x (v x (v x (v x u))) = -v Homework Equations The Attempt at a Solution I am very lost in this...

oh cause, the question asks Find all t such that the tangent line of the curve at (x(t), y(t)) intersects the x-axis at (4,0) so I'm assuming the t's I fins intersects the x-axis, so let say i plug in the t i find into the y(t) equation, shouldn't i get 0, but plugging in 1+squareroot(21)...

hey tiny-tim, for the preivous question, i don't think it's right cause i plugged in 1+squareroot(21) / 2 into t in y = e^t and i did not get 0...

thank you so much for the help!. I actually have one more question, Determine the values of t for which the curve x = 2squareroot(1+t), y = intergral from x to t^2 (squareroot(u) - 1)squareroot(1 + squareroot(u)) du, t greater and equal to 0 is concave upward and those for thich is it...

oh... i always thought that's the tangent line dy/dx then what i do now is e^t / 2t + 1 = e^t / t^2 + t - 4 and solve for t? which is ln t / 2t + 1 = ln t / t^2 + t - 4 t^2 + t - 4 / 2t + 1 = 1 t^2 - t - 5 = 0 using quadratic formula: comes out to be (1 + square root(21)) / 2...

omg what am i thinking, that's right m = y(t) - 0 / x(t) - 4 m = e^t / t^2 + t - 4 tangent at (x(t),y(t)): dy/dx = dy/dt / dx/dt = e^t / 2t + 1 x = t^2 + t, y = e^t so right right i fond the slop of the line according to t, how do i find the slop of the tangent line: x = t^2 +...

Thank you so much for the quick response, I was wondering, writing down the slope of the line from (4,0) to (x(t),y(t)), m = y(t) - 0 / x(t) - 4 tangent at (x(t),y(t)): dy/dx = dy/dt / dx/dt = e^t / 2t + 1 then I'm stuck hehe

Homework Statement a)Consider the parametric curve x = t^2 + t, y = e^t. Find all t such that the tangent line of the curve at (x(t), y(t)) intersects the x-axis at (4,0) Homework Equations The Attempt at a Solution I draw out the graph and came out with the points, I was wondering...