^ Quadratic interpolation formula

Three conditions for superheated steam provide the following accurate data for specific volume V^(m3/kg) and specific entropy S^(kJ/kgK) : (a) Compute the divided differences S^[V^2,V^1],S^[V^3,V^2], and S^[V^3,V^2,V^1] where S^[V^3,V^2,V^1]V^3V^1S^[V^3,V^2]S^[V^2,V^1]andS^[V^j,V^k]V^jV^kS^jS^k (b) Estimate the entropy at V^=0.118m3/kg by using the linear interpolation formula S^=b0+b1(V^V^i) Reminder: an easy way to find b0 and b1 is to pick one case as your first reference point i, plug in V^i and S^i, solve for b0, and then use your second point to obtain b1. Note: you should find that b1 equals one of the first two divided differences from above. (c) Estimate the entropy at V^=0.118m3/kg by using the quadratic interpolation formula S^=b0+b1(V^V^i)+b2(V^V^i)(V^V^j) Note: you should find that b2 equals the third divided difference from above. (d) Use inverse interpolation with the quadratic interpolation polynomial to determine the volume that corresponds to an entropy of 6.45kJ/kgK. .Inf(n)1 Inverse interpolation given f(x), what is x ? f(x)=b0+b1(xx0)+b2(xx0)(xx1) f2(x)=b0+b1(xx0)+b2(xx0)(xx1) where: b0=f(x0)b1=f[x0,x1]=x1x0f(x1)f(x0)b2=f[x0,x1,x2]=x2x0x2x1f(x2)f(x1)x1x0f(x1)f(x0) Three conditions for superheated steam provide the following accurate data for specific volume V^(m3/kg) and specific entropy S^(kJ/kgK) : (a) Compute the divided differences S^[V^2,V^1],S^[V^3,V^2], and S^[V^3,V^2,V^1] where S^[V^3,V^2,V^1]V^3V^1S^[V^3,V^2]S^[V^2,V^1]andS^[V^j,V^k]V^jV^kS^jS^k (b) Estimate the entropy at V^=0.118m3/kg by using the linear interpolation formula S^=b0+b1(V^V^i) Reminder: an easy way to find b0 and b1 is to pick one case as your first reference point i, plug in V^i and S^i, solve for b0, and then use your second point to obtain b1. Note: you should find that b1 equals one of the first two divided differences from above. (c) Estimate the entropy at V^=0.118m3/kg by using the quadratic interpolation formula S^=b0+b1(V^V^i)+b2(V^V^i)(V^V^j) Note: you should find that b2 equals the third divided difference from above. (d) Use inverse interpolation with the quadratic interpolation polynomial to determine the volume that corresponds to an entropy of 6.45kJ/kgK. .Inf(n)1 Inverse interpolation given f(x), what is x ? f(x)=b0+b1(xx0)+b2(xx0)(xx1) f2(x)=b0+b1(xx0)+b2(xx0)(xx1) where: b0=f(x0)b1=f[x0,x1]=x1x0f(x1)f(x0)b2=f[x0,x1,x2]=x2x0x2x1f(x2)f(x1)x1x0f(x1)f(x0)