c) sum n=0 ^ m a n x^ n If the power series converges uniformly in ] alpha, beta[ , then so does . True or false? Justify. sum n=0 ^ infty a n (-x)^ n
You have carried out an experiment to investigate the effect of the length of a pendulum not he time period of oscillation. Theory says that the pendulum should follow the rule:
T=2pi squarerootL/g
T is time period (seconds)
L is length of pendulum (metre)
G is acceleration due to gravity (9.81 m/s^2)
Calculate the expected percentage error in the time period calculation if your measurement is 2% high
Write the formula to find massof an object in 2-D coordinate system
Find the asymptotes of y^2(a+x) =x^2(3a-x) parallel to coordinate axes
Find the derivative of the given function.
1.) y = (x ^ 3 - 3)(x ^ 2 + 4x + 1)
2.) y = (7x + 3)(x ^ 4 - x ^ 3 - 9x)
3.) y = x ^ 2 * (2x ^ 2 + x + 1)
4.) y = (x ^ 2 - 10x + 2)(x ^ 3 - 2x ^ 2 + 1)
5.) y=(x^ 2 -2x-1)(x+)
6.) y= sqrt x( x^ 3 -2x^ 2 +7x-1)
7.) t = x ^ (1/3) * (x ^ 2 - 5x + 2)
8.) y = (5x ^ 2 - 13)(x ^ 3 + 6x + 1)
9.) y=x^ -2 (x^ 2 +7
10.) x ^ - 5 * (x ^ 2 + 10x - 5)
14. A rectangular water tank is being filled at a constant rate 20 liters/sec. the base of the tank has dimension W-1m, and L-2 m. What is the rate OF change of the height of water in the tanke? (Express the answer in cm/sec).
15 An airplane is flying in a straight direction and at a constant teight of STTY meters & The angle of elevation of the airplane from a fixed point of Observation is a. The speed of the airplane is stok /hr. what is the rate of charge of angle a when it is 25 degrees? (Express the answer in degrees /ceund) 18/12
7. Differentiate the function x = y ^ 4 - 2y ^ 3
8. Differentiate the function t = 1/2 * t ^ 4 - 5t - 3
9. Differentiate the function y = (x ^ 2 - 2) ^ 2
10. Differentiate the function y = 1/(x + 7)
11. Find the slope of function y = 1/(x ^ 2), 12, 1/4 12. Find the slope of function y^ 2 =4x.(1,2)
13. Find the slope of function y = 1/(x + 1), (- 2, 1)
find the centroid and boundaries y=x^2 and the line y=x
ACTIVITY IN BASIC CALCULUS
BASIC RULES IN DERIVATIVE
Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.
1. f(x) = -4x5+ ______x-4 - 2468
2. f (x) =____x-3- _____x1/4 - 12x
3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^6}{=} + \\frac{2}{3} x^6"
4.f (x) = "\\underset{x^-6}{=} -"____ x2 + "\\sqrt[4]{x}"
Find the lim r ̄(t), where t→1
sin(3t−3) r ̄(t)= t3, t−1 ,e2t