\( { \rm If} \ y = x^2 +7, { \rm \ differentiating} \ y \ {\rm with \ respect \ to} \ x\ {\rm gives}\)
\( x +7 \)
\( x +C , \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
\( 2x +7 \)
\( 2x \)
\(0.5 x^3 +C , \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
\( { \rm If} \ u = 2v^{-3} +6v, { \rm \ integrating} \ u \ {\rm with \ respect \ to} \ v\ {\rm gives}\)
\( -v^{-2} +3v^2 +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
\( -0.5v^{-4} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
\( -0.5v^{-4} +12v^2 \)
\( -4v^{-2} +12v^2 +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
\( -v^{-4} +C, \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
\( x = 3 \cos ( \pi t + \frac{2\pi}{3} ), \ {\rm find \ the \ value \ of } \frac{dx}{dt} {\rm when} \ t=1.0. \ Note \ the \ angle \ is \ measured \ in \ radians. \)
\( -0.86 \)
\( 8.2 \)
\( 0 \)
\( -2.6 \)
\( 1.5 \)
\( {\rm Calculate} \ J \ {\rm where} \ J= \int^{0.90}_{0}(17000 +12000x - 28000x^{2})dx \)
\(1.3 \times 10^{4} \)
\( -1.9\times 10^{3} \)
\( 4.6\times 10^{3} \)
\( 2.7\times 10^{4} \)
\( 1.2\times 10^{4} \)
\( {\rm Calculate} \ I, \ {\rm where} \ \epsilon = 17.6, {\rm \ is \ a \ constant \ and } \ I= \int^{0.47}_{-0.22}\frac{2\epsilon}{f^4}df . \)
\(-1.2 \times 10^{3} \)
\(-9.9 \times 10^{2} \)
\(3.9 \times 10^{2} \)
\(0 \)
\(-1.4 \times 10^{2} \)
