Survey of Calculus II Exam 2 Latest
Update With Complete Solutions
d(x^n)/dx CORRECT ANSWERS nx^n-1
d(lnx)/dx CORRECT ANSWERS 1/x
d(e^x)/dx CORRECT ANSWERS e^x
d[f(x)/g(x)]/dx CORRECT ANSWERS [f'(x)g(x)-f(x)g'(x)]/[g(x)]^2
d(f(x)g(x))/dx CORRECT ANSWERS f'(x)g(x)+f(x)g'(x)
d(f(g(x)))/dx CORRECT ANSWERS f'(g(x))g'(x)
Second Derivative Test CORRECT ANSWERS D(x,y)=fxxfyy-(fxy)^2
Relative Maximum CORRECT ANSWERS D(a,b)>0 & fxx(a,b)<0
Relative Minimum CORRECT ANSWERS D(a,b)>0 & fxx(a,b)>0
Saddle Point CORRECT ANSWERS D(a,b)<0
Test is Inconclusive CORRECT ANSWERS D(a,b)=0
Method of Lagrange Multipliers CORRECT ANSWERS F(x,y,lambda)=f(x,y)
+lambda(g(x,y))
Change in f CORRECT ANSWERS f(x+change in x, y+change in y)-f(x,y)
df CORRECT ANSWERS fxdx+fydy
f(x1,y1) CORRECT ANSWERS df+f(x2,y2)
Average Value CORRECT ANSWERS SSf(x,y)dA/SSdA
Integration by Parts CORRECT ANSWERS Sudv=uv-Svdu
u CORRECT ANSWERS simpler when differentiated
dv CORRECT ANSWERS easily integrated
Update With Complete Solutions
d(x^n)/dx CORRECT ANSWERS nx^n-1
d(lnx)/dx CORRECT ANSWERS 1/x
d(e^x)/dx CORRECT ANSWERS e^x
d[f(x)/g(x)]/dx CORRECT ANSWERS [f'(x)g(x)-f(x)g'(x)]/[g(x)]^2
d(f(x)g(x))/dx CORRECT ANSWERS f'(x)g(x)+f(x)g'(x)
d(f(g(x)))/dx CORRECT ANSWERS f'(g(x))g'(x)
Second Derivative Test CORRECT ANSWERS D(x,y)=fxxfyy-(fxy)^2
Relative Maximum CORRECT ANSWERS D(a,b)>0 & fxx(a,b)<0
Relative Minimum CORRECT ANSWERS D(a,b)>0 & fxx(a,b)>0
Saddle Point CORRECT ANSWERS D(a,b)<0
Test is Inconclusive CORRECT ANSWERS D(a,b)=0
Method of Lagrange Multipliers CORRECT ANSWERS F(x,y,lambda)=f(x,y)
+lambda(g(x,y))
Change in f CORRECT ANSWERS f(x+change in x, y+change in y)-f(x,y)
df CORRECT ANSWERS fxdx+fydy
f(x1,y1) CORRECT ANSWERS df+f(x2,y2)
Average Value CORRECT ANSWERS SSf(x,y)dA/SSdA
Integration by Parts CORRECT ANSWERS Sudv=uv-Svdu
u CORRECT ANSWERS simpler when differentiated
dv CORRECT ANSWERS easily integrated
