Answer: d=13
Step-by-step explanation:
d+13=26
d=13
If this wasn't what you asked for please rephrase the question. Thank you!
Answer:
![f(x)=x+\dfrac{x^{3}}{3}+\dfrac{2x^{4}}{3}....](https://tex.z-dn.net/?f=f%28x%29%3Dx%2B%5Cdfrac%7Bx%5E%7B3%7D%7D%7B3%7D%2B%5Cdfrac%7B2x%5E%7B4%7D%7D%7B3%7D....)
Approximate error = 0.4426
Step-by-step explanation:
f(x)=tanx, a=0
Maclaurin series formula used is given below
![f(x)=\sum_{n=0}^{\infty}\dfrac{f^{(n)}(0)x^{n}}{n!}=f(0)+f'(0)x+\dfrac{f''(0)}{2!}x^{2}+\dfrac{f'''(0)}{3!}x^{3}+....](https://tex.z-dn.net/?f=f%28x%29%3D%5Csum_%7Bn%3D0%7D%5E%7B%5Cinfty%7D%5Cdfrac%7Bf%5E%7B%28n%29%7D%280%29x%5E%7Bn%7D%7D%7Bn%21%7D%3Df%280%29%2Bf%27%280%29x%2B%5Cdfrac%7Bf%27%27%280%29%7D%7B2%21%7Dx%5E%7B2%7D%2B%5Cdfrac%7Bf%27%27%27%280%29%7D%7B3%21%7Dx%5E%7B3%7D%2B....)
f(x)=tanx
f(0)=tan0=0
![f'(x)=sec^{2}x\\f'(0)=sec^{2}0=1\\f''(x)=2sec^{2}xtanx\\f''(0)=2sec^{2}0tan0=0\\f'''(x)=-4sec^{2}x+6sec^{4}x\\f'''(0)=-4sec^{2}0+6sec^{4}0=-4+6=2\\](https://tex.z-dn.net/?f=f%27%28x%29%3Dsec%5E%7B2%7Dx%5C%5Cf%27%280%29%3Dsec%5E%7B2%7D0%3D1%5C%5Cf%27%27%28x%29%3D2sec%5E%7B2%7Dxtanx%5C%5Cf%27%27%280%29%3D2sec%5E%7B2%7D0tan0%3D0%5C%5Cf%27%27%27%28x%29%3D-4sec%5E%7B2%7Dx%2B6sec%5E%7B4%7Dx%5C%5Cf%27%27%27%280%29%3D-4sec%5E%7B2%7D0%2B6sec%5E%7B4%7D0%3D-4%2B6%3D2%5C%5C)
![f''''(x)=-8(2sec^{2}xtan^{2}x+sec^{4}x)+24(4sec^{4}xtan^{2}x)+sec^{6})\\f''''(0)=-8(0+1)+24(0+1)=-8+24=16\\](https://tex.z-dn.net/?f=f%27%27%27%27%28x%29%3D-8%282sec%5E%7B2%7Dxtan%5E%7B2%7Dx%2Bsec%5E%7B4%7Dx%29%2B24%284sec%5E%7B4%7Dxtan%5E%7B2%7Dx%29%2Bsec%5E%7B6%7D%29%5C%5Cf%27%27%27%27%280%29%3D-8%280%2B1%29%2B24%280%2B1%29%3D-8%2B24%3D16%5C%5C)
![f(x)=0+x+0+\dfrac{2x^{3}}{3!}+\dfrac{16x^{4}}{4!}\\](https://tex.z-dn.net/?f=f%28x%29%3D0%2Bx%2B0%2B%5Cdfrac%7B2x%5E%7B3%7D%7D%7B3%21%7D%2B%5Cdfrac%7B16x%5E%7B4%7D%7D%7B4%21%7D%5C%5C)
![f(x)=x+\dfrac{x^{3}}{3}+\dfrac{2x^{4}}{3}\\](https://tex.z-dn.net/?f=f%28x%29%3Dx%2B%5Cdfrac%7Bx%5E%7B3%7D%7D%7B3%7D%2B%5Cdfrac%7B2x%5E%7B4%7D%7D%7B3%7D%5C%5C)
Hence, the Taylor series for f(x)=tanx is given by
![f(x)=x+\dfrac{x^{3}}{3}+\dfrac{2x^{4}}{3}....](https://tex.z-dn.net/?f=f%28x%29%3Dx%2B%5Cdfrac%7Bx%5E%7B3%7D%7D%7B3%7D%2B%5Cdfrac%7B2x%5E%7B4%7D%7D%7B3%7D....)
Maclaurin series upper bound error formula used is given as
R_n(x)=|f(x)-T_n(x)|
R_3(x)=|tanx-T_3(x)|
![R_3(x)=|tanx-x-\dfrac{x^{3}}{3}-\dfrac{2x^{4}}{3}|](https://tex.z-dn.net/?f=R_3%28x%29%3D%7Ctanx-x-%5Cdfrac%7Bx%5E%7B3%7D%7D%7B3%7D-%5Cdfrac%7B2x%5E%7B4%7D%7D%7B3%7D%7C)
Plugging this value x=1
![R_3(x)=|tan(1)-1-\dfrac{1}{3}-\dfrac{2}{3}|\\](https://tex.z-dn.net/?f=R_3%28x%29%3D%7Ctan%281%29-1-%5Cdfrac%7B1%7D%7B3%7D-%5Cdfrac%7B2%7D%7B3%7D%7C%5C%5C)
R_3(x)=|1.5574-1-0.333-0.666|
R_3(x)=|-0.4426|=0.4426
Hence, upper bound on the error approximation
tan(1)=0.4426
It would be equal to 0.45 = 45/100 = 9/20
so, your answer is 9/20
Answer:
the lowest amount mia can spend is $75
Step-by-step explanation:
3x12=36
12x3+15 this is for the noise makers
9 x 4= 36
15 x 4 = 60
60+15=75
she will spend 75 dollars on party suplies
Your question has been heard loud and clear.
The difference between 18 hrs and 50 mins and 13hrs and 45mins is
5 hours and 5 minutes.
Thank you