4. Referring to the remainder in the characterization of differentiation, show that r(y) --+ 0 as...
15 PTS) 2. Use implicit differentiation to show that x + y +exy = 0 is an implicit solution to the nonlinear equation (1 + xexy)*%+1+ yexy = 0. dx
Consider d on R defined by
d(x, y) = ?|x − y|.
(1) Show that (R, d) is a metric space.
(2) Show that the path γ(t) = t, t ∈ [0, 1] has infinite
length.
Remark: On (2), you only need to verify by the partitions of
equal distances. Although this is slightly different from the
actual definition, it indeed implies that length equals to
infinity, by using some techniques in the Riemann sum (e.g.
refining a partition). This...
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
4. Let = 0 , 4r + 2y+-2). M={(x,y,z) € R' | - Show that A/ is a one dimensional manifold and find the maximum and minimum values of SIM where f(x,y, z) = ry + z.
explicit differentiation
find f'(y)
explicit differentiation
b) In x® + Belly + lng = 0 b) In x® + Belly + In š = 0
Show that the cigenvalue probom (ry' (r))' = Ary(r), 0 <r<R, y(0) is bounded, y(R) = 0 has no negative eigenvalues. Hint: Use an energy argument.
The monotonicity property of the integral implies that if the functions g,h : 0,00) → R are continuous and g(x) S h(x) for all x 2 0, then ghfor all r 2 0. 0 0 Use FTC1 to show that each one of the following inequalities implies its successonr: cosx <1 if r 0 1 - cosr if x 0 2 3 > if r 20 Hence
The monotonicity property of the integral implies that if the functions g,h :...
Finish the proof of Theorem 3.14.
Theorem 3.14 Let (neN aand EneN be sequences in R. Let be in R# and suppose that x" → x, y, → oo, and z" →-oo. . If -oo <x o, then +yn 2. If-oo x < 00, then x" + Zn →-00 4. If-oo x < 0, then xoY" →-00 and xnZn → oo. 5. If x is in R. then-→0and-" →0 Proof Note that the conditions in the different parts of the...
Question 15 Use implicit differentiation to find if: x In(y + 2) + y2 = 0 дх Ay+2 + x2 y + x2 + x2 8.-(4+2) In(y + 2) x + y + y2 C. None of the answers D. (x + 2) In(x + 2) y + x2 + x2 E-(*+7+42 x + y2 + y2
show works , thank you
P UULIU1 10 15 . 4. (dpt) Use logarithmic differentiation to find if y=(2 + cos r)"/2.
ho Find y' if y=r=sin(wy). Hint: Use implicit differentiation