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Show that the series 8/(n⁴+x⁴) is uniformly convergent for all real values of x. n=1 to infinity .
n the right triangle ABC, AB = 2, BC = 4 and ED is a line parallel to AB. Find the
angle α = angle BAD which minimizes the distance L, where L = AD + ED
The number of claim per hour at the WBA Insurance Company has a Poisson distribution with mean 3 claim per hour. Find the probability that in any given hour there will be.
a) exactly none claims
b) exactly one claim
c) exactly two claims
d) three or more class
e) exactly four claims in 2 hours
Let the operations * and ⊕ be defined on the set of integers.
Find each of the following are commutives, associatives, left-distributive, and right-distributive.
1. a*b=ab; a⊕b=-a-b
2. a*b=a+2b; a⊕b=a-2b
3. a*b=2ab; a⊕b=2a+2b+4ab
4. a*b=-a-b-2ab; a⊕b=3a+3b
5. x*y=x2+2x+y2; x⊕y=x+y
A game of chance entails three coins. For each head that comes up, the player receives Ksh 1000 and loses Ksh 800 for any tail that comes up. To play the game, one pays Ksh 1500.
Advise a player whether it is advisable to play the game.
c) Describe geometrical meaning of definite integral with figure.
a) Define differentiation and integration in calculus. Also write down the
differences between them.
Find an orthonormal basis of R^3 of which (1√10,0,-3/√10) is one element
3. a) Define tangent and normal of a curve with figure. Also find the equation of tangent and normal of the ellipse (x ^ 2)/4 + (y ^ 2)/16 = 1 at the point (- 1, 3) .
b) Explain maximum and minimum value of a function with graphically. Evaluate maximum and minimum value of the function f(x) = x ^ 3 - 3x ^ 2 + 3x + 1
5. a) Calculate the area under the curve y = x ^ 3 + 4x + 1 from x = - 3 to x = 3 .
b) Evaluate: integrate x * e ^ x dx from 0 to 4
#340153 on Dec 2023