Chapter - 4

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 Page - 79

Exercise - 4

Solution:

 #include<iostream>  
 using namespace std;  
 int factorial(int n){  
   if(n==0){  
     return 1;  
   }  
   return n * factorial(n-1);  
 }  
 int main(){  
 float r;  
 cout<<"Enter value of 'r' "<<endl;  
 cin>>r;  
 float ans =0;  
 for(int i=1;i<=r;i++){  
   if((i&1)==0){  
     ans+=factorial(r)/factorial(i) ;  
   }else{  
     ans-=factorial(r)/factorial(i);  
   }  
 }  
 cout<<ans;  
 }  

Solution:

 #include<iostream>  
 #include<cmath>  
 using namespace std;  
 float rot(int n){  
   if(n==0){  
     return 0;  
   }  
   return sqrt(2+rot(n-1));  
 }   
 int main(){  
   int n;  
   cout<<"Enter number of iteration of n"<<endl;  
   cin>>n;  
   float ans =1;  
   for(int i=1;i<=n;i++){  
     ans*=rot(i)/2 ;  
   }  
   cout<<"from RHS 'solving eqaution' we get : "<<ans<<endl;  
   cout<<"from LHS '2/pi' we get : "<<2/M_PI<<endl;  
 }  

Solution:

 #include<iostream>  
 #include<cmath>  
 using namespace std;  
 float power(int a ,int b){  
   if(b==0){  
     return 1;  
   }  
   return a*power(a, b-1);  
 }  
 int factorial(int n){  
   if(n==0){  
     return 1;  
   }  
   return n * factorial(n-1);  
 }  
 int main(){  
   float x;  
   cout<<"Input value of 'x' : "<<endl;  
   cin>>x;  
   float ans=0;  
   for(int i=0;i<15;i++){  
     ans+=power(x,i)/factorial(i);  
   }  
   cout<<"by solving RHS equation : "<<ans<<endl;  
   cout<<"by solving LHS 'e^x' : "<<exp(x);  
 }  

Solution:

 #include<iostream>  
 using namespace std;  
 int power(int x , int i){  
   if(i==0){  
     return 1;  
   }  
   return x* power(x,i-1);  
 }  
 int main(){  
   cout<<"Enter number of coefficient : ";  
   int n;  
   cin>>n;  
   int coeff[n];  
   cout<<"input coeffecients in increasing order of power of x..."<<endl;  
   cout<<"For example: A1 X^n , A2 X^2....An X^n"<<endl;  
   for(int i=0;i<n;i++){  
     cin>>coeff[i];  
   }  
   cout<<"Input value of 'x' "<<endl;  
   int x;  
   cin>>x;  
   float ans=0;  
   for(int i=0 ; i<n;i++){  
     ans=ans+coeff[i]*power(x,i);  
   }  
   cout<<ans;  
 }  

Solution:

 #include<iostream>  
 using namespace std;  
 int main(){  
   cout<<"Enter number of coefficient : ";  
   int n;  
   cin>>n;  
   int coeff[n];  
   cout<<"input coeffecients in decreasing order of power of x..."<<endl;  
   cout<<"for exampal : An X^n , An-1 X^n-1...A1 X1"<<endl;  
   for(int i=0;i<n;i++){  
     cin>>coeff[i];  
   }  
   cout<<"Input value of 'x' "<<endl;  
   int x;  
   cin>>x;  
   float ans=0;  
   for(int i=0;i<n;i++){  
     if(i>1){  
       ans=ans*x+coeff[i];  
     }else{  
     ans+=x*coeff[i];}  
   }  
   cout<<"answer is : "<<ans;  
 }  

Solution:

 #include<iostream>  
 using namespace std;  
  int main(){  
    int d;  
    cout<<"input value of d : ";  
    cin>>d;  
    int n;  
    cout<<"input number of digit in nuber m : ";  
    cin>>n;  
    int ans =0;  
   cout<<"input number m (space between in digits of number m)"<<endl;  
   while(n--){  
     int m;  
     cin>>m;  
     if((d*m)>9 && ans>1){  
       ans=(ans+(d*m/10))*10+((d*m)%10);  
     }else{  
     ans=ans*10 + d*m ;  
     }  
   }  
   cout<<"your answer is "<<ans;  
  }