f(x) = (x^2+x+3)^48 (x^3+5x-2)^84 f'(x)=?

f(x) = (x^2+x+3)^48 (x^3+5x-2)^84 f'(x)=?

48(2x+1)(x^2+x+3)^47(x^3+5x-2)^84+84(3x^2+5)(x^2+x+3)^48(x^3+5x-2)^83
That should be it,

Alevel math? 1.P is the point (7.5) and L1 is the line with equation 3x+4y=16 (1).Find out the equation of the line L2 which passes through P and is perpendicular to L2. (2).Find the point of intersection of the L1 and L2. (3).Find the perpendicular distance of P from the line L1.

(1) Permanent to L1?
L2:4x-3y=13
(2)(4,1)
(3)d=(/3*7+4*5-16/)/5=5
(1) Q is the straight line L2 that has been found P and is perpendicular to L1
(2) Q is to find the intersection of L1 and L2
(3) Q is to find the distance from P to L1

Simplify the expasion of（1-x)^8+(1+x)^8 including the term in x^2,by putting x=0.01,find the approprizte value of 0.99^8+1.01^8,correct to three decimal places.

（1-x)^8+(1+x)^8 = 2(1+8C2x^2 + 8C4x^4+8C6x^6+x^8)=2(1+ 28x^2+70x^4+28x^6+x^8)= 2+ 56x^2 ( including the term in x^2)x=0.010.99^8+1.01^8 = 2+56(0.01)^2=2.0056=2.006 ( 3decimal places)

Translate a math problem in English Phillip charged $400 worth of goods on his credit card. On his first bill, he was not charged any interest, and he made a payment of $20. He then charged another $18 worth of goods. On his second bill a month later, he was charged 2% interest on his entire unpaid balance. How much interest was Phillip charged on his second bill? A. $8.76 B. $7.96 C. $7.60 D. $7.24 E. $6.63

(400-20+18)*2%=7.96
The answer is B.
Paid 20 and spent 18, so the actual cost was 398

Using the pinch theorem, it is proved that if A1, A2, A3,... Am are m normal numbers, then Under the root sign of LIM (n tends to ∞) n, A1 ^ n + A2 ^ n +. + am ^ n = a, where a = max {A1, A2,., am} Using the convergence criterion that the monotone bounded sequence must have a limit, it is proved that if X1 = root 2, X2 = 2 + root 2, and xn + 1 = 2 + xn (n = 1,2,.), LIM (n tends to ∞) xn exists, and the limit is solved

Question 1: replace all A1, A2,..., am with A. in this way, the whole formula is enlarged, and the result is
Under n-th root sign (n * a ^ n) = under n-th root sign (n) * a, the limit is a
Then reduce the formula. There must be one equal to a in A1, A2,..., am. Leave this item and delete the rest. In this way, it will be reduced. The result is: under the n-th root sign (a ^ n) = a
The limit after enlargement and reduction is a, which is proved by the pinch criterion
In the second question, we must first prove the existence of the limit. It is obvious that the single increase of the sequence is bounded,
Mathematical induction, x1

1. Sin ^ 2 (2x) is the square of sin 2x 2.∫(sin^x cos^x)

1. Transformed into an integral of sin (4x)
2. Transformed into an integral of sin (2x)