9000064807 Level: CFind the sum of the integers which satisfy the following inequality. x2−8x−153≤0108162917856
9000064008 Level: CFind the limit of the following sequence. ((n2+2n+1)nn2n)n=1∞ Hint: The limit of the sequence ((1+1n)n)n=1∞ is the Euler number e.e22ee+2∞
9000064009 Level: CFind the limit of the following sequence. ((2nn+2n)n)n=1∞ Hint: The limit of the sequence ((1+1n)n)n=1∞ is the Euler number e.2ee2e+2∞
9000064010 Level: CFind the limit of the following sequence. ((2n+1n)n)n=1∞ Hint: The limit of the sequence ((1+1n)n)n=1∞ is the Euler number e.∞2ee2e+2
9000063303 Level: CDifferentiate the following function. f(x)=sinxf′(x)=cosx2sinx, x∈⋃k∈Z(2kπ;π+2kπ)f′(x)=sinx2cosx, x∈⋃k∈Z(2kπ;π2+2kπ)f′(x)=12sinx, x∈⋃k∈Z(2kπ;π+2kπ)f′(x)=cosx2sinx, x∈⋃k∈Z[2kπ;π2+2kπ]
9000063304 Level: CDifferentiate the following function. f(x)=lnxf′(x)=12x, x>0f′(x)=12x, x≠0f′(x)=1x, x>0f′(x)=1x, x≠0
9000063305 Level: CDifferentiate the following function. f(x)=x−1x+1f′(x)=1(x+1)2x+1x−1, x∈(−∞;−1)∪(1;∞)f′(x)=x−1(x−1)2x+1, x∈(−∞;−1)∪[1;∞)f′(x)=x−12(x+1)3, x≠−1f′(x)=x−1(x+1)3, x∈(−∞;−1)∪[1;∞)
9000063306 Level: CDifferentiate the following function. f(x)=esin2xf′(x)=2esin2xcos2x, x∈Rf′(x)=xesin2xcos2x, x∈Rf′(x)=esin2xsin2x, x∈Rf′(x)=ecos2x, x∈R
9000063307 Level: CDifferentiate the following function. f(x)=ln(cos2x)f′(x)=−2tg2x, x∈⋃k∈Z(−π4+kπ;π4+kπ)f′(x)=2tg2x, x∈⋃k∈Z(−π4+kπ;π4+kπ)f′(x)=−2, x∈⋃k∈Z(−π4+kπ;π4+kπ)f′(x)=1−ln(sin2x), x∈⋃k∈Z(kπ;π2+kπ)