Calculus Answers

Use Weierstrass’ M-Test to prove that the series
Infinity
∑ n^2x^n
n=1
converges uniformly in
the interval .
[0,1/5]

(1 point) Find d2ydx2 for
y=csc(x)
d2ydx2=

Prove that between any two real roots of the equation
2e^2xsin3x-3=0

There is at least one real root of the equation
e^2xcos3x+1=0

Test the absolute and conditional convergence of the series

Infinity
∑ (-1)^n/(2n+1)
n=1

Let a function :f R → R be defined by

f(x)={2 if x∉Q
4 if x∈Q}

Check whether f is continuous on B.

check whether the set [−3,7 [∩]− 7,3
]is a neighbourhood of 2 or not.

Cauchy’s general principle of convergence for sequences. To check whether the
sequence (1/2n)
is convergent or not.

All strictly monotonically decreasing sequences are convergent.

True or false

For all even integral values of n, ( )
n,
lim(x +1)^-n
X→∞
exists.
State True or false

you have been given the mathematical model to calculate velocity of a car accelerating from rest in straight line: v(t) = A (1-e ^ - t/tmaxspeed) (anything after the symbol ^ is to the power of) v(t is instantaneous velocity of car (m/s), t is time in seconds, tmaxspeed is time to reach maximum speed in seconds and A is constant. you are given the information that t (0-28 m/s) is 2.6s, t (400m) is 10.46s & tmaxspeed is 7s. Apply the mathematical model above to the car, use given data for the 0-28m/s and 400m times to calculate: value of the coefficient A, maximum velocity and maximum acceleration? please show graphs for this information aswell