Math1Z03 Sample Test1 2013

Suppose is differentiable on s let tanc find an

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: DQG Z ² ³ ~  ILQG D E F G FRV % H c FRV %  % % ²%³(%~ H  /HW 8²%³ ~ - ²%³°´.²%³µ  ZKHUH - DQG . DUH WKH IXQFWLRQV ZKRVH JUDSKV DUH VKRZQ )LQG 8Z ² ³ LI LW H[LVWV D c E c F c G H  6XSSRVH WKDW  ² ³ ~ c Á  Z ² ³ ~ Á ² ³ ~ Á DQG Z ² ³ ~ c  )LQG ´°² b ³µZ ² ³ D E F G H  )LQG D VLPSOLILHG H[SUHVVLRQ IRU & Z D ² b ³ ° E ² b ³ ° F  ² b ³ &~ °  j b G  b H   b  )LQG &Z LI & ~ %FRV % D %FRV % OQ h ²FRV % c %VLQ %³ E %FRV % %FRV %c OQ h ²FRV % c %VLQ %³ F %FRV % ²FRV % c %VLQ %³ G %FRV % ²FRV %%VLQ %³ H %FRV % %FRV %c ²FRV % c %VLQ %³  )LQG Z ²%³ LI ²%³ ~ j FRV² %³ b j WDQ % D cj VLQ² %³ b ² WDQ %³c ° h WDQ % E cj VLQ² %³ h b ² WDQ %³c ° h WDQ % h VHF % F cj VLQ² %³ h b ² WDQ %³c ° h WDQ % h WDQ % VHF % G cj VLQ² %³ h b ² WDQ %³c ° h WDQ % h VHF % H cj VLQ² %³ b ² WDQ %³c ° h WDQ % h VHF %  )LQG D simplified H[SUHVVLRQ IRU WKH GHULYDWLYH RI  ²%³ ~ %  D % c °% G %c °% ² b %³ E c °% ² % c c ³ H c °% ² % c ³  If  ²%³ b % ´ ²%³µ ~ D c E F % c °% c °% ²% b ³ and  ² ³ ~ , find  Z ² ³. F c G c  If  ²%³ ~ ln²ln %³ , find  Z  . D   E F  G ln H c H   Find an equation of the tangent line to  ²%³ ~ ln²ln %³ at the point ²Á ³. D & ~  % c E & ~ % c  F & ~  % b  G & ~ H & ~c %   Differentiate  ²%³ ~ ln4 D cjln % 5. E c jln % %jln %² cjln %³ H %jln %² c jln %³ F cjln % %jln % G %jln %² cjln %³ .  Suppose  is differentiable on s Let - ²%³ ~  ²tanc ´% µ³. Find an expression for - Z ²%³ D  Z ²tanc ´% µ h F  Z ²tanc ´% µ³ h H  Z ²tanc ´% µ³ h %% ³ b % % % b% %% b % E  Z ²tanc ´% µ³ h %% G  Z ²tanc ´% µ³ h %% b%  Let  ²%³ ~ c % . Starting with % ~ , compute % using Newton's method. D E F G H  Suppose the line & ~ % c is tangent to the curve & ~  ²%³ when % ~ . If Newton's method is used to locate a root of the equation  ²%³ ~ and the initial approximation is % ~ , find the seco...
View Full Document

This document was uploaded on 03/24/2014 for the course MATH 1Z03 at McMaster University.

Ask a homework question - tutors are online