Answer question number 8 4Gılll Gilll17:0295%+ M5_Application of...Find the differentials of the following:1. z = V- 3x2. r =Find the first and second derivative of y with respect to x from the parametric equations given.3. x =T y = t? + 34. x = VT-i; y = t - 3t5. x = VE+ 2; y = t² - 3Evaluate the limit of the following6. lim sincas Sx7.lim lansin x8. lim(0 sin9. The base of a right triangle is fixed at 3ft.the hypotenuse is 5ft. long and subject to change. Findthe approximate change in altitude when hypotenuse is changed by small amount Ah.10. The diameter of circle is measured and found to be 6ft with a maximum error of 0.1 in. Find theapproximate maximum error in the computed area.11. Find the change in the lateral surface area of a right circular cone, with radius of base fixed as r,when the altitude h changes by a small amount Ah.12. The position of an object at time t is given by x = V3t – 4 ++4, where x is in feet and t is inseconds. What are the object's velocity, acceleration and total distance travel at time t = 1?13. A ball is thrown upward from the ground with a speed of 40ft/sec; at the same instant anotherball is dropped (from rest) from a height of 100ft. Show that they strike the ground at the same time.14. Given the parametric equation below determine the total velocity and acceleration at t = 2x(t) = v -+t and y(t) = t? – 2VE + 315. Find two numbers whose sum is a, it the product of one by the cube of the other is to be maximum.MODULE 5 APPLICATION OF DERIVATIVES25ENGINEERING CALCULUS 116. A sphere is cut to shape a circular cone. How much of the material can be saved?17. Find the most economical proportions for a cylindrical cup.18. A rectangular field of fixed area is to be enclosed and divided into three lots by parallel to one sides.What should be the relative dimensions of the field to make the amount of fencing?19. A wall 10 ft high is 8ft from the house. Find the length of the shortest ladder that will reach thehouse, when one end rest on the ground outside the wall.20. A triangular trough is 10ft long, 6 ft across the top, and 3 ft deep. If water flows in at the rate of3ft. /min, find how fast the surface is rising when the water is 6 in. deep.21. A ladder 20 ft long leans against the wall. If the top slides downward at the rate of 2ft/sec, howfast the lower ends is moving when it is 16ft from the wall.22. A man 6ft tall walks away from a lamp post 16ft high at the rate of 5 mi/hr. How fast does theshadow lengthen?23. A train, starting at noon, travels north at 40 mi/hr. Another train, starting from the same point at2 PM, travels east at 50mi /hr, how fast the two trains are separating at 3PM.24 A Fght ot ouo louol ctande 20ft irom the boure ancft from the path londingthe hou

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Description: Answer question number 8 4Gılll Gilll17:0295%+ M5_Application of...Find the differentials of the following:1. z = V- 3x2. r =Find the first and second derivative of y with respect to x from the parametric equations given.3. x =T y = t? + 34. x = VT-i