Q. Write a function power, which calculates x^y . Write another function, which calculates n! Using for loop. Use these functions to calculate the sum of first n terms of the Taylor series
Taylor series: sin(x) = x - x^3/3! + x^ 5 /5!
Program
#include<stdio.h>
#include<math.h>
void cal();
void main()
{
cal();
}
void cal()
{
int x,i;
int fact = 1,n;
float sum=0;
printf("\nEnter the value of x in the series : ");
scanf("%d",&x);
printf("\nEnter the number of terms in the series : ");
scanf("%d",&n);
for(i=1;i<n;i++)
{
fact = fact*i;
sum = sum + (pow(x,i)/fact) ;
}
sum= sum +1;
printf("\nThe sum of the taylor series is : %.2f\n\n",sum);
}
Output:
Enter the value of x in the series : 4
Enter the number of terms in the series : 6
The sum of the taylor series is : 42.87
Taylor series: sin(x) = x - x^3/3! + x^ 5 /5!
Program
#include<stdio.h>
#include<math.h>
void cal();
void main()
{
cal();
}
void cal()
{
int x,i;
int fact = 1,n;
float sum=0;
printf("\nEnter the value of x in the series : ");
scanf("%d",&x);
printf("\nEnter the number of terms in the series : ");
scanf("%d",&n);
for(i=1;i<n;i++)
{
fact = fact*i;
sum = sum + (pow(x,i)/fact) ;
}
sum= sum +1;
printf("\nThe sum of the taylor series is : %.2f\n\n",sum);
}
Output:
Enter the value of x in the series : 4
Enter the number of terms in the series : 6
The sum of the taylor series is : 42.87
1 Comments
def gcd(a, b):
ReplyDeletewhile b:
a, b = b, a % b
return a
def display_state(jug1, jug2):
print(f"{'JUG 1: ':>11}{jug1:<6} | {'JUG 2: ':>12}{jug2}")
def pour_water(jug1, jug2, capacity1, capacity2):
pour_amount = min(jug1, capacity2 - jug2)
jug1 -= pour_amount
jug2 += pour_amount
return jug1, jug2
def water_jug_solution(capacity1, capacity2, target_amount):
jug1 = 0
jug2 = 0
print(f"Jug 1 Capacity: {capacity1} | Jug 2 Capacity: {capacity2}")
while jug1 != target_amount and jug2 != target_amount:
if jug1 == 0:
jug1 = capacity1
elif jug2 == capacity2:
jug2 = 0
else:
jug1, jug2 = pour_water(jug1, jug2, capacity1, capacity2)
display_state(jug1, jug2)
first_jug = int(input("Enter the capacity of the first jug: "))
second_jug = int(input("Enter the capacity of the second jug: "))
target_amount = int(input("Enter the target liters of water: "))
if target_amount < first_jug or target_amount < second_jug:
if target_amount % gcd(first_jug, second_jug) == 0:
water_jug_solution(first_jug, second_jug, target_amount)
else:
print("This is not possible....")
else:
print("This is not possible....")