lim as h->0 of (f(x+h) - f(x))/h or lim as x->a of (f(x) - f(a))/(x - a)
f(x) = x/2Then the differential is lim h->0 [f(x+h) - f(x)]/h= lim h->0 [(x+h)/2 - x/2]/h= lim h->0 [h/2]/h= lim h->0 [1/2] = 1/2f(x) = x/2Then the differential is lim h->0 [f(x+h) - f(x)]/h= lim h->0 [(x+h)/2 - x/2]/h= lim h->0 [h/2]/h= lim h->0 [1/2] = 1/2f(x) = x/2Then the differential is lim h->0 [f(x+h) - f(x)]/h= lim h->0 [(x+h)/2 - x/2]/h= lim h->0 [h/2]/h= lim h->0 [1/2] = 1/2f(x) = x/2Then the differential is lim h->0 [f(x+h) - f(x)]/h= lim h->0 [(x+h)/2 - x/2]/h= lim h->0 [h/2]/h= lim h->0 [1/2] = 1/2
The derivative of f(x) is lim h-->0 [f(x+h)-f(x)]/h. So let f(x) = -5x. The derivative is lim h-->0 [-5(x+h)- -5(x)]/h = lim h-->0 [-5x - 5h + 5x]/h = lim h-->0 -5h/h Since the limit h-->0 of h/h is 1, the derivative is -5
Yes. You can make sense of this by referring to the definition of a derivative:f'(x) = lim h goes to 0 of (f(x+h)-(fx))/hAs long as f(x+h) (as h goes to 0), and f(x) are defined so is f'(x). In fact, the only way f' is defined is if f(x) is defined.
Apply the reciprocal rule: If f(x) = 1/h(x) then f'(x) = -h'(x)/(h(x))^2
#include<stdio.h> #include<conio.h> #include<math.h> #define f(x) (sin(x*x)) void main() { float a,b,h,x,s,n,aaa,h1,h2,p=0.0,p1=0.0,pp,sum,k,i=0.0; int j=1,co; clrscr(); printf("\n Plese Enter lower limit :"); scanf("%f",&a); printf("\n Plese Enter upper limit :"); scanf("%f",&b); printf("\n Plese Enter the number of Intervales::"); scanf("%f",&n); h=(b-a)/n; //Calculiting the value of h printf("The ..................=%f",h); x=a+h; s=f(a)+f(b); //Calculiting the First term & last term while(j<n) { if((j%2)==0) //checking even and odd terms i=i+(2*f(x)); //Calculiting the even terms else i=i+(4*f(x)); //Calculiting the odd terms x=x+h; j++; } i=(h/3)*(i+s); //putting all data in to the formula printf("\nThe value of the integral is %f",i); // part is for Error calculation h1=b-h; h2=a+h; pp=(7*(f(h2)+f(h1))); sum=a-h; k=b+h; x=a+(2*h); for(co=2;co<n-2;co++) { if(co%2==0) p=p+(f(x)); else p1=p1+(f(x)); x=x+h; } aaa=(-(h/90))*( ( f(sum)+f(k) )-4*(s) +7*( f(h1) )-(8*p)+(8*p1) ); printf("\nThe Error is= %f",aaa); getch(); }
The letter that have parallel line in it are H,I,F
H. C. Prange Co. ended in 1992.
H. C. Prange Co. was created in 1881.
William H. Block Co. was created in 1896.
William H. Block Co. ended in 1987.
lim as h->0 of (f(x+h) - f(x))/h or lim as x->a of (f(x) - f(a))/(x - a)
Co (like in co-worker) hairor co (like in co-worker) h (hard h) eh(short e) r
A function f(x) is not differentiable at x=a if: lim h-->0 [f(a+h)-f(a)] / h does not exist.
No published sn data I know of.
1. H-H 2. H-I 3. H-Br 4. H-Cl 5. H-F
F. H. Jackson died in 1960.