maths work

CAN ANY OF YOU DO BOTH FILES IN A PERFECT MANNER WITRHIN 7 HRS ? REPLY ASAP.

Quiz 8 MATH

1

910 Calculus I Name:

This quiz is due at the beginning of class Monday November 18. On separate paper, please write your
solutions neatly and show your work in an organized manner. No credit will be given for answers without
supporting work or for solutions presented in a disorganized manner which renders it difficult for me to
follow. You do not need to turn in this sheet with your work.

Theorem 1. If f is integrable on [a, b], then∫ b
a

f (x)dx = lim
n→∞

n∑
i=1

f (xi)∆x

where ∆x =
b − a

n
and xi = a + i∆x.

1. Evaluate the integral using the above Theorem.∫ 3
−1

(2 − x − 5×2)dx

2. Evaluate the above integral using the Fundamental Theorem of Calculus.

3. A particle is moving with the given data. Find the position of the particle.
a(t) = sin t + 3 cos t , s(0) = 0 , v(0) = 2

4. Use Newton’s method with the specified intial approximation x1 to find x3 , the third approximation
to the root of the given equation. (Give your answer to four decimal places)
x7 + 4 = 0 , x1 = −1

END

1

1. fj What value of the constant c will make the following limit exist?

[(
2X + [x I) ]M~ x (x2 + C – 2)

following statements are true and give an explanation to justify your answer.

1

-6 -5 -4 -3 -2 -1 o 1 2 3 4 5 6

-1

(a). limx–>_2 f(x) = 1
(b).f( -2) = f(2)

-( \

(c). y = 3 is a horizontal asymptote of [,

(d).f'(l) = 4

(e). [is not differentiable at three values ofx.

(f). limX-.l [(x) = [(1)

(g). f’ (-3) + f’ (2.5) = 0

3. 4••• ~Find :~ for the following functions. Simplify your solution if possible.

(a). y = 41n(x2 – 3x + 4)
(b). y = xtan(x)

(c). y = e21n(X)

4. ~ One bicyclist is 4 miles east of an intersection and is traveling toward the
intersection at a rate of9 mph. At the same time, a second bicyclist is 3 miles south of the
intersection and is traveling away from the intersection at a rate of 10 mph. Is the distance
between the two bicyclists increasing, or is it decreasing? At what rate is the distance changing?

5..~ -‘ -~ Finding an equation of the line tangent to the following curves at the given point.

(a). y = 4×5 + cos x; X = 0

(b). xy +.JXY = 6; (x,y) = (1,4)