Linear Approximation of a Function Near a Point. A very important and useful approximation: For c near 0, Assuming that a is near 0, use the above approximation to find an approximation for the following functions. 1 f(I) = 1+ 2x f(x) = V5 -8. ~ M In Einstein's corrected formula, mass has the value m = where M represents the mass of an object at rest, v represents the 1 velocity of the object, and c is the speed of light. If we assume that v is small compared with c then, we can fin an approximation to the mass of the object to be: mThe Differential of a Function. Find the differential of the given function. Then, evaluate the differential at the indicated values. If y = 6x- + 15x + 4 then the differential of y is dy Note: Type dx for the differential of c Evaluate the differential of y at co = 1 , de = 0.5 dy I TO ar 0.5 Note: Enter your answer accurate to 4 decimal places if it is not an Integrer.The Differential of a Function. Find the differential of the given function. Then, evaluate the differential at the indicated values. If y = x cos (#) then the differential of y is dy Note: Type dx for the differential of x Evaluate the differential of y at co = -14.1372 , da = 0.6 dy dr 0.6 Note: Enter your answer accurate to 4 decimal places if it is not an Integrer.The Differential of a Function. Find the differential of the given function. Then, evaluate the differential at the indicated values. If y = 13 312 then the differential of y is VI47 dy Note: Type dx for the differential of r Evaluate the differential of y at co = 3 , de = 0.4 dy dr 0.4 Note: Enter your answer accurate to 4 decimal places if it is not an Integrer.Poiseville's Law states that the volume, V, of blood flowing through an artery in a unit of time at a fixed pressure is directly proportional to the fourth power of the radius of the artery. That is, V = krs, where r is the radius of the artery. If the radius is increased by about 7 %, by about how much will the volume of blood flowing through the artery increase? By about how much must the radius of the artery be increased to achieve a 45 % increase in the volume of blood flowing through the artery? % Note: enter an answer accurate to 4 decimal places.Suppose the side length of a cube is measured to be 11.4 cm with a possible error in measurement of 1 0.05 cm. Use differentials to estimate the error in the computed volume of the cube. The approximate absolute error is: The approximate percentage error is: Note: enter an answer accurate to 4 decimal places.An astronaut using a camera measures the radius of the Earth as 3982 mi with an error of 1 100 mi. Using differentials, estimate the relative and percentage error of using this radius measurement to calculate the volume of the Earth, assuming the planet is a perfect sphere. The approximate relative error is: The approximate percentage error is: % Note: enter an answer accurate to 4 decimal places.A surveying team set up some equipment 139 it from the base of a tree in order to sight the top of the tree. From ground level, they measure the angle of elevation to be 29". If the calculated height needs to be accurate to within 2%, what is the allowed error in the angle measurement? (Assume the 139 ft measurement is 100% accurate.) The allowed relative error is The allowed percent error is % Note: enter an answer accurate to 4 decimal places