\f\f{1 paint] Find the equation of the line that is tangent tn the eunre )1 = xmex at the point (1:, \"63). The equation etthie tangent Iineean be written in the farm 3; = nu: + b where a! amb=' ::: .5! {1 point} Use Implicit dlerentiation to nd the slope utthe tangent line to the curve dened by 1379 -+- 5x): = 18 at the paint (3, l). The slope of the tangent lineto the curve atthe given point 3 {1 point] Find the slope of the tangent line to the curve 25in(x} + 2 0050:) - 5 sin(x) (2050:) + x = 35 at the point (33'. 31:12). | 555 I y {1 point) Helium is pumped into a spherical balloon at a rate of 4 cubic feet per second. How fast is the radius increasing after 3 rninLItes'lI Note: The volume of a sphere is given by V = (4J3)n'r3. Flats of change of radius [in feet per second) = l H! J {1 point) The radius of a spherical balloon is increasing at a rate of 4 centimeters per minute. How fast is the volume changing when the radius is 8 centimeters? Note: The volume of a sphere is given by V = (4.8)m-3. l it! Fists of change of volume = i {1 point) Use linear approximation. is. the tangent line. to approximate 1,149.1 as follows: Letx) = JE. The equation ofthe tangent line tox) at x = 49 can be written in the town 3: = m): + b where m is: and where b is: 5 Using this. we find our approximation for V491 is NOTE: For this part. give your answer to at least 9 signicant gures or use fractions to give the exact answer i it! {1 point) Use linear approximation. Le. the tangent line. to approximate ; as follows: Letx) = i and find the equation of the tangent line tef(x) at a 'nice' point near 0.10]. Then use 1 0.10] this to appIOXImate m