d) Consider the series
. Now the ratio,
Thus the series to be convergent we need . Which
is the interval of convergence , although it is a point.
5. Given knots a-to <t1 < < tn-b, and data points (ti, yi), for i - 0,... ,n, prove the clamped cubic spline S satisfying S,(a)-a, S,(b) satisfies for all g E C2[a,b] interpolating the data points and satisfying g'(a)-α, g'(b)-β
5. Given knots a-to
A programmable thermostat allows you to select 4 tîmes, 0 < T1 T424 (for a 24-hour cycle) and the corresponding setpoint temperatures a1, . ,04. Con struct a timed automaton that sends the event ai to the heating systems controller The controller maintains the temperature close to the value a; until it receives the next event. How many timers and modes do you need?
10. Let T1 and T2 be two topologies on a set X. Then T1 is said to be a finer topology than T2 (and T2 is said to be a coarser topology than T1) if Ti2 T2. Prove that (i) the Euclidean topology R is finer than the finite-closed topology on R; (ii) the identity function f: (X, Ti) -(X, T2) is continuous if and only if TI is a finer topology than T2.
L. iT D C Cr ve İT It--+ t3 t4 12 0 t3 t4 t) 0 to ti
Tanks T1 and T2 both initial contains 50 gallons of pure water. Starting at t = 0, water that contains 1 pound of salt per gallon is poured into Ti at a rate of 2 gal/min. The mixture is drained from T1 at the same rate into the second tank T2. Starting at to = 0, a mixture from another source that contains 2 pounds of salt per gallon is poured into T2 at a rate of 2 gal/min. The...
3. The complex [Ti(H20)6]3+ is violet, while the analogous complex with another monodentate neutral ligand L, [Ti(L)6]3+ is orange. How many of the following statements are true? Explain briefly. (a) L is a stronger field ligand than H20. (b) [Ti(L)6]3+ is a high-spin complex. (c) [Ti(L)6]3+ absorbs yellow and red light. (d) Both complexes have two 3d electrons associated with the metal.
0 6 ti
A uniform plank of mass 30kg and length 20m is supported by two
ropes T1 and T2 attached as shown on the diagram. Two masses 20kg
and 25kg are suspended are shown to keep the plank in equilibrium.
Find the tension T1 and T2 due to the two ropes.
I'm having trouble with this question. Would love to see the
actual work, so I can understand the concept.
4. A uniform plank of mass 30 kg and length 20 m,...
Consider the following MIPS machine code. bne $0, $0, 2 addi $t0, $0, 5 addi $t1, $0, 10 What will be in $t0 and $t1 after the above program is executed? a. $t0 = 5, $t1 is unknown because 3rd statement will not be executed b. $t1 = 10, $t0 is unknown because 2nd statement will not be executed c. $t0 = 5, $t1 = 10 d. $t0 = 0, $t1 = 0
Prove that sequence 2, 3 ... ti converges to l.