10. [0/0.214 Points] DETAILS PREVIOUS ANSWERS LARCALC11 12.5.036 Find the curvature K of the curve. r(t) = esti + est cost j+ est sin t k 26 e -57 V K= 57 X Need Help? Read ItSketch the space curve. Vector-Valued Function Interval r(t) = (2 sin t, 4t, 2 cos t) [0, 7] 10 3 Z 1.0 5 U.O. 0.0. - 0.5 1.0 -1.0 -2.9.5.0. 3PE OF -10 Subuo - 2 0 1 2 Find its length over the given interval. 4V2.Sketch the space curve. Vector-Valued Function Interval r(t) = (2 sin t, 4t, 2 cos t) [0, 7] 10 3 Z 1.0 5 U.O. 0.0. - 0.5 1.0 -1.0 -2.9.5.0. 3PE OF -10 Subuo - 2 0 1 2 Find its length over the given interval. 4V2.4. [0/0.068 Points] DETAILS PREVIOUS ANSWERS LARCALC11 12.2.014. Find r'(t) r(t) = 4\\ti + +2ti + In(+2)k ( V7 ) = - 1 r'(t) = 2V/7. X Need Help? Read It Watch It 5. [-/0.068 Points] DETAILS LARCALC11 12.2.015. Find r'(t) r(t) = e"'i+ 4j + 9tek r'(t) = -e it di + (get + 9te )k Need Help? Read It Watch It Viewing Saved Work Revert to Last Response16. [0.14/0.273 Points] DETAILS PREVIOUS ANSWERS LARCALC11 12.2.038. Find - [r(t) . u(t)] and -" [r(t) * u(t)] in two different ways. r(t) = cos ti + sin tj + tk, u(t) = j+ tk (a) [r(t) . u(t)] (i) Find the product first, then differentiate. t+ cost + t (ii) Apply the properties of the derivative. cost + 2t (b) [r(t) * u(t)] (i) Find the product first, then differentiate. (ii) Apply the properties of the derivative. Need Help? Read It17. [-/0.068 Points] DETAILS LARCALC11 12.2.039. Find the indefinite integral. (Use c for the constant of integration.) ( 2ti + 1 + 8k ) at ritti + 8k+ c Need Help? Read It Watch It Viewing Saved Work Revert to Last Response 18. [-/0.068 Points] DETAILS LARCALC11 12.2.040. Find the indefinite integral. (Use c for the constant of integration.) (41 3 1 + 101) - 3Vtk) at fi+ 5t j - 2NV 7k+ c Your answer cannot be understood or graded. More Information X Need Help? Read It Viewing Saved Work Revert to Last Response 19. [0/0.068 Points] DETAILS PREVIOUS ANSWERS LARCALC11 12.2.046. Find the indefinite integral. (Remember to use absolute values where appropriate. Use c for the constant of integration.) ( e " sin (t)i + cot (t)i ) dt ( cost - sint) + In sin t X Need Help? Read It20. [0/0.068 Points] DETAILS PREVIOUS ANSWERS LARCALC11 12.2.048. Evaluate the definite integral. X Need Help? Read It 21. [0/0.068 Points] DETAILS PREVIOUS ANSWERS LARCALC11 12.2.050.MI. Evaluate the definite integral. The [(sect tan thi + (tan t)j + (2 sin t cos t)k dt V2 + [In( (2) -1) ] Need Help? Read It Watch It Master It 22. [0/0.068 Points] DETAILS PREVIOUS ANSWERS LARCALC11 12.2.052. Evaluate the definite integral. 88 3 X Need Help? Read It Watch It