Answer:
x=1
y=s
z=1
Step-by-step explanation:
(x, y, z)=(1, 0, 1)
Substitute 0 for y
Confirming if t=0 satisfy the other equation
x = e^−2t cos 4t = e^−2(0)cos(4*0)
= e^(0)cos(0) = 1
z = e^−2t = e^−2(0) = 0
Therefore t=0 satisfies the other equation
Finding the tangent vector at t=0
The vector equation of the tangent line is
(1, 0, 1) +s(0,1,0)= (1, s, 1)
The parametric equations are:
x=1
y=s
z=1
Answer:
Correct integral, third graph
Step-by-step explanation:
Assuming that your answer was 'tan³(θ)/3 + C,' you have the right integral. We would have to solve for the integral using u-substitution. Let's start.
Given : ∫ tan²(θ)sec²(θ)dθ
Applying u-substitution : u = tan(θ),
=> ∫ u²du
Apply the power rule ' ∫ xᵃdx = x^(a+1)/a+1 ' : u^(2+1)/ 2+1
Substitute back u = tan(θ) : tan^2+1(θ)/2+1
Simplify : 1/3tan³(θ)
Hence the integral ' ∫ tan²(θ)sec²(θ)dθ ' = ' 1/3tan³(θ). ' Your solution was rewritten in a different format, but it was the same answer. Now let's move on to the graphing portion. The attachment represents F(θ). f(θ) is an upward facing parabola, so your graph will be the third one.
