# Must remember x x lnd x 1 and if u is a

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MUST REMEMBER!!! xxlnDx1and if uis a differentiable function of x, uDuulnDxx1TO DO!!!Solve for  x'f. 1.  xtanxseclnxf2.  3xsinxlnxfHOW TO . . . derive the derivative of xln!! ! xdttxln11(area of a region bounded by xy1) If 10x, then 0xln. If 1x, then 0xln. If 1x, then 0xln. xxxdttDxlnD11(By the Fundamental Theorem of the Calculus)
MATH 37 Lecture Guide UNIT 1 albabierra 8 KEEN MIND HERE!!!Why Cxlndxx1, instead of xln? Problem:Domain of x1: Domain of xln: Solution:00xifxxifxxxxlnDx1xlnDxMUST REMEMBER!!! xalnxlogDax11and if uis a differentiable function of x, uDxalnulogDxax11TO DO!!! Evaluate .xloglogDx2110MUST REMEMBER!!! Cxlndxx1and if uis a differentiable function of x, CulnuduMATH MODELS. Nerve impulses in the human body travel along nerve fibers that consist of an axon,which transports the impulse, and a insulating coating called the myelin sheath.Nodes of Ranvierserve as relay stations along the fibers; however, between nodes the nerve fiber is similar to an insulated cylindrical cable. It is known that for such cables, the velocity vof an impulse is given by xlnkxv2where xis the ratio of the radius of the cable and the insulation radius. Find the value xthat maximizes v. (In most nerve, x0.6) TO DO!!! Evaluate the following 1. baxdxwhere aand bare constants
MATH 37 Lecture Guide UNIT 1 albabierra 9 Exercise Items. Try to solve the following. Solve for dxdy. 1. 5213xxlny5. 111xlnxySimplify!2. xsinxcoslogy1010106. 1xyyxln3. 3247235xxlny7. 22yxxylog4. 332xlnlogy8. 123222xyyxlnx(Curve sketching)Using the First Derivative Test and the Second Derivative Test, sketch the graph of  xlnxxf. Also, determine the relative extrema and inflection points of the graph. 2. dxxx16423. xdxtan_____________________________ How to solve for dxxsinxcosxsinxcos? MUST REMEMBER!!!Integrals of the “Other” Trigonometric FunctionsCxseclndxxtanCxcsclndxxcotCxtanxseclndxxsecCxcotxcsclndxxcscThese are easy to verify by differentiating the right sides! MATH MODELS.Determine the area of the region bounded by xcscyand xcotyfrom 4xto 2x.
MATH 37 Lecture Guide UNIT 1 albabierra 10