MTH101 Quiz 3 by Iqra Azhar

(1^2)+(2^2)+(3^2)+……………..+(50^2) equals--------NOTE: x^n means ‘x’ to the power ‘n’ n(n+1)(2n+1)/6 50(50+1)(2×50+1)/6 42925

Summation of 2 where sum ranges from 0 to 10 equals 20. t f If you add 2 ten times, you get 2×10=20 ∑ i=0 to10 2=20 So, the statement is true,

Which geometrical figure is used for approximating the area under the curve? Trapezoid

The area between f(x)=-x and the closed interval [-1,0] on x-axis is ---------- Area=∫−1 0(−x)dx Area=[− x 2/2]−1 0 -1/2

for n = 2 is ________.

=∑ i=1 3 f(x i )⋅Δx Δx= b−a/n a=1, b=3, and n=2. Δx=1 f(x)=x ^2 at the right endpoints of the subintervals: =∑ i=1 3 f=1+4+9 =13 =13*1 By applying mean value theorem to the functionf(x)=lnx in the interval [1,e], the corresponding value of ‘c’ is ------------(Hint: lne=1, ln1=0) Now, apply the Mean Value Theorem: f(c)= f(b)−f(a)/b−a f(x)=ln(x) f (c)= f(e)−f(1)/ e−1 f (c)= ln(e)−ln(1)/e−1

Which of the following will be left end points if the interval [-2,2] is divided into 4 equal subintervals −2,−1,0,1.

To find the area between continuous curve f(x) and the closed interval [a,b] on x-axis, we take-------------- of f(x) on the interval [a,b]. integrate the absolute value of the function

By using Newton method, which of the following is the poorest initial approximate solution of equation:x+Cosx=0?

doesn't converge or divergence.

Integral of 3sec(x)tan(x) is NOTE: x^n means ‘x’ to the power ‘n’ sec(x)tan(x)dx. This will simplify the integral. 3sec(x)+C, where

Given f(x)= 1/(x-1) on the interval (0,3) , then ‘f ’ has no relative maxima or relative minima due to……… Open interval Discontinuity in the interval Rational function none of " Discontinuity in the interval." he integral ∫cot(2x)dx nwill be equal to ln∣sin(2x)∣+C,

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = definite integral of ‘1’ on closed interval [0,1], then the value of ‘a’=------------

na

a a a x a a f ‘n’ goes from 1 to 4 and the summation of ‘na’ =Maxima of (e^x) in the interval[-e,0], then the value of ‘a’ is -----------

^ 0 0,

/10 Maxima of e x in The maxi na a a a a a a mum occurs at x so

a a

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = 6a, then the value of ‘a’ is -

na a a a a a a a undefine

1+2+3+…+539 equals _____. S n= n/2 (2a+(n−1)d) a=1, d=1, n=539. =145,530