Postgraduate Mathematics II task 19: For f(x)=5x³+6x², enter f′(4).
f′(x)=15x²+12x. Substituting x=4 gives 288.
Practice china-kaoyan-math-2 questions with answers and explanations.
f′(x)=15x²+12x. Substituting x=4 gives 288.
An antiderivative is 4/2 x²+5x. At x=5, the value is 75.0.
The dot product is 4×2+6×4=32.
Rewrite the value using base 5: 3125 = 5^5. Matching exponents gives x = 5.
Choose an option to check your answer.
Use the circle-area formula A = πr². Substituting r = 9 gives A = π × 9² = 81π.
Percentage=(14/29)×100=48.28.
Subtract 7 from both sides and divide by 7: x = (63-7)/7 = 8.
Choose an option to check your answer.
The sum is n(n+1)/2=36, so the mean is 36/8.
Choose an option to check your answer.
There are 6 favourable outcomes out of 12 equally likely outcomes, so P(red)=6/12.
The dot product is 3×4+5×3=27.
Rewrite the value using base 4: 256 = 4^4. Matching exponents gives x = 4.
Choose an option to check your answer.
Use the circle-area formula A = πr². Substituting r = 8 gives A = π × 8² = 64π.