FURTHER MATHS
posted by FLORENCE .
STATE THE LINEAR APPROXIMATION FOR: (2.04)raise to power 5

There are lots of possible approximations. If we have
y = x^5, the slope of the tangent line is
y' = 5x^4
At (2,32), the slope is 80
so, if a(x) is the line,
a(x) = 80(x2)+32
a(2.04) = 80(.04)+32 = 35.2
In fact, 2.04^5 = 35.33
Respond to this Question
Similar Questions

calculus
se differential, i.e., linear approximation, to approximate (8.4)^(1/3) as follows: Let f(x)=(x )^(1/3). The linear approximation to f(x) at x=8 can be written in the form y=mx+b where m is: and where b is: Using this, we find our … 
Math (linear approximation)
Find a linear approximation of the function f(x)=(1+x)^(1/4) at a=1, and use it to approximate the numbers (.95)^(1/4) and (1.1)^(1/4). Round your answers to the nearest thousandth Cheers in advance! 
Math
a.) Given that f(3)=5 and f'(x)=x/((x^3)+3), find the linear approximation of f(x) at x=3. b.)If the linear approximation is used to estimate the value of f(2.9), will it be an overestimation or underestimation? 
Calculus
a.) Given that f(3)=5 and f'(x)=x/((x^3)+3), find the linear approximation of f(x) at x=3. b.)If the linear approximation is used to estimate the value of f(2.9), will it be an overestimation or underestimation? 
mechanics of materials
A metal bar with a crosssectional area of 50mm2 is subjected to a tensile strain of 0.001. What is the tensile force responsible for the strain given that the material has a Young's modulus of 15GNm raise to the power 2 A 0.003N … 
linear approximation
a) Find the linear approximation of the function f(x)=4cos(3x^2) near x = 0 b) Use the approximation found in part (a) to estimate the value of f(pi/20) 
Math
Use differential, (i.e. linear approximation), to approximate cube root of 64.1 as follows: Let f(x) = cube root of x. The linear approximation to f(x) at x = 64 can be written in the form y = mx+b. Compute m and b and find cube root … 
CALCULUS
If the local linear approximation of f(x) = 3sin x + e3x at x = 2 is used to find the approximation for f(1.9), then the % error of this approximation is 
math
Suppose f(x)=ln x. (a) Find the linear approximation of f at a=1. L(x)= (b) Use the linear approximation to estimate ln 1.27. ln1.27= 
MATHS
SIMPLIFY SIN RAISE TO POWER 4 MINUS COS RAISE TO POWER4 DIVIDED BY 1 MINUS 2SIN RAISE TO POWER 2