EXAMPLE 6 Calculate lim x cot(x). x 0 SOLUTION uling x cot(x) = _ Here we...
Rewrite cot (cos-'v) as an algebraic expression in v. cot (cos 'v) = 0 x 6 ?
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...
0/6 POINTS LARPCALC10 5.2.010. Verify the identity. (Simplify at each step.) tan x cot x = sec X COS X tan x cotx COS X = sec X COS X Submit Answer
Use this definition of a right-hand limit to prove the following limit. EXAMPLE 3 x0 SOLUTION and L such that 1. Guessing a value for 6. Let & be a given positive number. Here a = so we want to find a number 0 x6 if then that is if 0 <x<6 then <E or, raising both sides of the inequality to the eleventh power, we get 0 <x if then x < This suggests we should choose 8= 2....
9 نقاط Find the particular solution to the : differential equation y" +('+ x)cot x = 0 when y = 1 and - = 0 ع إضافة ملف
please if you know how to due this its due today
6. Consider the wave equation on the sphere of radius 1 with c 1 Ou + cot θου t.csc 26-y _P.1 Write the solution for initial conditions u(9:9,0) = 4 sin θ cos θ cos φ and cos θ θ, φ,0) =
6. Consider the wave equation on the sphere of radius 1 with c 1 Ou + cot θου t.csc 26-y _P.1 Write the solution for initial conditions...
Using the example above as a guide, find all solutions to the equation - 2 cos(0) - 1 = - 1.5 on the domain 0 <o<2. [Note that this is an equation involving the cosine function, not the sine function.] Use commas to separate your answers if there is more than one solution. radians
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Find the solution to the initial value problem: x(0)-0x(O)--1 x(t) write x(t) as a product of a sine and a cosine, one with the beat (slow) frequency (μ-2)/2 , and the other with the carrier (fast) frequency (μ+ 2)/2 x(t) The solution x(t) is really a function of two variables t and μ . Compute the limit of x(t씨 as μ approaches 2 (your answer should be a function of t. lim x(t,H) Define y(t)-lim x(t,u) What differential...
line response. lin0g(x).-3. Namethelimitruiesthatareusedto steps (a) (b), and (c) of the following calculation. x-0 (f(x) +15) 1/2 (b) lim -f)- lim 3gt)(1 lim fix) -3 lim g) lim (-1f(x) -3g(x)) lim (f(x) 15) x--0 (c) x-0 x--0 lim fx)+lim 15)1/2 l (y 15)12( ( 15)1/2 A) (a) Difference Rule (b) Power Rule (c) Sum Rule B) (a) Quotient Rule C) (a) Quotient Rule D) (a) Quotient Rule (b) Difference Rule (c) Constant Multiple Rule (b) Difference Rule, Power Rule (c)...
We can expect the solution u(x,y) to be in the form
X(x)Y(y).
or
I believe that these are the correct forms of X(x) and Y(y).
2. Laplace's equation Consider Laplace's equation on the rectangle with 0 < x < L and 0 < < H: PDE BC BC BC u(x,0) 0, u(z, H) = g(z). (10) where a mixture of Dirichlet and Neumann boundary conditions is specified, and only one of the sides has a boundary condition that is nonhomogeneous...