MTH281: Mathematical Method I TMA1

[embeddoc url=”https://naijablog.ng/wp-content/uploads/2018/05/qustion-t-1.pptx” download=”all” viewer=”microsoft”]

Question 1 : Forg(x)=x−4x−3, we can use the mean value theorem on [4, 6], Hence determine c
A.√112
B.c=2±√2
C.c=3±√3
D.c=−2±√5

Question 2 : If the functionf(x)=tan−1xy, finddfdx
A.yx2−y
B.xx2−y2
C.xx2+y2
D.2yx2−y2

Question 3 : Evaluate thed3fdx3d3fdx3off(x)=sin(x)cos(x)f(x)=sin(x)cos(x)
A.d3fdx3=−4(cos2(x)−sin2(x))
B.d3fdx3=−4(tan2(x)−cos2(x))

C.d3fdx3=−2(Cos2(x)+sin2(x)) D.f′(x)=5×4−12×12+12×2,20×3−34x−12−1×1,100×2−38x−32+3×4

Question 4 : Determine whether the mean value theorem can be applied toffon the closed interval [a, b] . If can be applied, Find the value ofccin open interval (a, b) such thatf(x)=x(x2−x−2),[−1,1]
A.c=−13
B.c=−25
C.c=−12
D.c=−23

Question 5 : Letf(x)=x4−2×2. Find the allcc(whereccis the interception on the x-axis ) in the interval (-2, 2) such thatf′(x)=0f. ( Hint use Rolle’s theorem )
A. (-1, 1, 1)
B. (-1, 0, 1)
C. (-1, 0, 2)
D. (-1, 2, 1)

Question 6 : Evaluate thelimx→2×2+4x−12×2−2x
A. 4
B. 1
C. 3
D. 2

Question 7 : Find the two x-intercept off(x)=x2−3x+2
A. x=1, 1
B. x=-2, 2
C. x=3, 1
D. x=1, 2

Question 8 : Givenf(x)=3x(x−1)5. Computef′′′(x)f‴(x)
A.180(x−1)2(2x−1)
B.2i−j
C.80(2x−1)2(x−1)
D.100(x−1)2(4x−1)100

Question 9 : Find the numberccguaranteed by the mean value theorem for derivatives forf(x)=(x+1)3,[−1,1]
A.c=−√(2)±1√(3)
B.c=−√(3)±2√(3)
C.c=−√(5)±2√(5)
D.c=−√(5)±2√(5)

Question 10 : Determine whether the Rolle’s theorem can be applied toffon the closed interval [a, b] . If can be applied, Find the values ofccin open interval (a, b) such thatf′(c)=0f′(c)=0,f(x)=x2−2x−3x+2
A.c=−2±2√(5)
B.c=−2±√(5)
C.c=−1±√(5)
D.c=−2±√(5)