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Linearization Of Trigonometric Functions

Determine the linear approximation of $f\left(x\right)=\sin\left(x\right)$ at a=0.

$L\left(x\right)=x$

$L\left(x\right)=-x$

$L\left(x\right)=0$

Determine the linear approximation of $f\left(x\right)=\sec\left(x\right)$ at a=0.

$L\left(x\right)=\sec\left(1\right)+\sec\left(1\right)\tan\left(1\right)\left(x-1\right)$

$L\left(x\right)=\sec\left(1\right)+\sec\left(1\right)\tan\left(1\right)$

$L\left(x\right)=\sec\left(1\right)$

Determine the linear approximation of $L\left(x\right)=\tan\left(x\right)$ at a=-1.

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x+1\right)$

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)$

Determine the linear approximation of at a=1.

$L\left(x\right)=\cos\left(1\right)$

$L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)\left(x-1\right)$

$L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)\left(x+1\right)$

Determine the linear approximation of $f\left(x\right)=\sin\left(x\right)$ at a=-1.

$L\left(x\right)=\sin1$

$L\left(x\right)=\sin\left(1\right)+\cos\left(1\right)\left(x+1\right)$

$L\left(x\right)=\sin\left(1\right)+\cos\left(1\right)$

Determine the linear approximation of at a=-1.

$L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)\left(x+1\right)$

$L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)$

$L\left(x\right)=\cos\left(1\right)$

Determine the linear approximation of $f\left(x\right)=\cot\left(x\right)$ at a=1.

$L\left(x\right)=\cot\left(1\right)-\csc^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\cot\left(1\right)+\csc^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\cot\left(1\right)+\csc^2\left(1\right)\left(x+1\right)$

Determine the linear approximation of $f\left(x\right)=\cot\left(x\right)$ at a=-1.

$L\left(x\right)=\cot\left(1\right)-\csc^2\left(1\right)\left(x+1\right)$

$L\left(x\right)=\cot\left(1\right)-\csc^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\cot\left(1\right)+\csc^2\left(1\right)\left(x-1\right)$

Determine the linear approximation of $f\left(x\right)=\sec\left(x\right)$ at a=0.

$L\left(x\right)=2$

$L\left(x\right)=1$

$L\left(x\right)=0$

Determine the linear approximation of at a=1.

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)$

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x+1\right)$

Questions

Time

Score

Linearization Of Trigonometric Functions

Determine the linear approximation of ﻿f(x)=sin⁡(x)f\left(x\right)=\sin\left(x\right)f(x)=sin(x)﻿ at a=0.

﻿L(x)=xL\left(x\right)=xL(x)=x﻿

﻿L(x)=−xL\left(x\right)=-xL(x)=−x﻿

﻿L(x)=0L\left(x\right)=0L(x)=0﻿

Determine the linear approximation of ﻿f(x)=sec⁡(x)f\left(x\right)=\sec\left(x\right)f(x)=sec(x)﻿ at a=0.

﻿L(x)=sec⁡(1)+sec⁡(1)tan⁡(1)(x−1)L\left(x\right)=\sec\left(1\right)+\sec\left(1\right)\tan\left(1\right)\left(x-1\right)L(x)=sec(1)+sec(1)tan(1)(x−1)﻿

﻿L(x)=sec⁡(1)+sec⁡(1)tan⁡(1)L\left(x\right)=\sec\left(1\right)+\sec\left(1\right)\tan\left(1\right)L(x)=sec(1)+sec(1)tan(1)﻿

﻿L(x)=sec⁡(1)L\left(x\right)=\sec\left(1\right)L(x)=sec(1)﻿

Determine the linear approximation of ﻿L(x)=tan⁡(x)L\left(x\right)=\tan\left(x\right)L(x)=tan(x)﻿ at a=-1.

﻿L(x)=tan⁡(1)+sec⁡2(1)(x+1)L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x+1\right)L(x)=tan(1)+sec2(1)(x+1)﻿

﻿L(x)=tan⁡(1)+sec⁡2(1)(x−1)L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x-1\right)L(x)=tan(1)+sec2(1)(x−1)﻿

﻿L(x)=tan⁡(1)+sec⁡2(1)L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)L(x)=tan(1)+sec2(1)﻿

Determine the linear approximation of at a=1.

﻿L(x)=cos⁡(1)L\left(x\right)=\cos\left(1\right)L(x)=cos(1)﻿

﻿L(x)=cos⁡(1)+sin⁡(1)(x−1)L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)\left(x-1\right)L(x)=cos(1)+sin(1)(x−1)﻿

﻿L(x)=cos⁡(1)+sin⁡(1)(x+1)L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)\left(x+1\right)L(x)=cos(1)+sin(1)(x+1)﻿

Determine the linear approximation of ﻿f(x)=sin⁡(x)f\left(x\right)=\sin\left(x\right)f(x)=sin(x)﻿ at a=-1.

﻿L(x)=sin⁡1L\left(x\right)=\sin1L(x)=sin1﻿

﻿L(x)=sin⁡(1)+cos⁡(1)(x+1)L\left(x\right)=\sin\left(1\right)+\cos\left(1\right)\left(x+1\right)L(x)=sin(1)+cos(1)(x+1)﻿

﻿L(x)=sin⁡(1)+cos⁡(1)L\left(x\right)=\sin\left(1\right)+\cos\left(1\right)L(x)=sin(1)+cos(1)﻿

Determine the linear approximation of at a=-1.

﻿L(x)=cos⁡(1)+sin⁡(1)(x+1)L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)\left(x+1\right)L(x)=cos(1)+sin(1)(x+1)﻿

﻿L(x)=cos⁡(1)+sin⁡(1)L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)L(x)=cos(1)+sin(1)﻿

﻿L(x)=cos⁡(1)L\left(x\right)=\cos\left(1\right)L(x)=cos(1)﻿

Determine the linear approximation of ﻿f(x)=cot⁡(x)f\left(x\right)=\cot\left(x\right)f(x)=cot(x)﻿ at a=1.

﻿L(x)=cot⁡(1)−csc⁡2(1)(x−1)L\left(x\right)=\cot\left(1\right)-\csc^2\left(1\right)\left(x-1\right)L(x)=cot(1)−csc2(1)(x−1)﻿

﻿L(x)=cot⁡(1)+csc⁡2(1)(x−1)L\left(x\right)=\cot\left(1\right)+\csc^2\left(1\right)\left(x-1\right)L(x)=cot(1)+csc2(1)(x−1)﻿

﻿L(x)=cot⁡(1)+csc⁡2(1)(x+1)L\left(x\right)=\cot\left(1\right)+\csc^2\left(1\right)\left(x+1\right)L(x)=cot(1)+csc2(1)(x+1)﻿

Determine the linear approximation of ﻿f(x)=cot⁡(x)f\left(x\right)=\cot\left(x\right)f(x)=cot(x)﻿ at a=-1.

﻿L(x)=cot⁡(1)−csc⁡2(1)(x+1)L\left(x\right)=\cot\left(1\right)-\csc^2\left(1\right)\left(x+1\right)L(x)=cot(1)−csc2(1)(x+1)﻿

﻿L(x)=cot⁡(1)−csc⁡2(1)(x−1)L\left(x\right)=\cot\left(1\right)-\csc^2\left(1\right)\left(x-1\right)L(x)=cot(1)−csc2(1)(x−1)﻿

﻿L(x)=cot⁡(1)+csc⁡2(1)(x−1)L\left(x\right)=\cot\left(1\right)+\csc^2\left(1\right)\left(x-1\right)L(x)=cot(1)+csc2(1)(x−1)﻿

Determine the linear approximation of ﻿f(x)=sec⁡(x)f\left(x\right)=\sec\left(x\right)f(x)=sec(x)﻿ at a=0.

﻿L(x)=2L\left(x\right)=2L(x)=2﻿

﻿L(x)=1L\left(x\right)=1L(x)=1﻿

﻿L(x)=0L\left(x\right)=0L(x)=0﻿

Determine the linear approximation of at a=1.

﻿L(x)=tan⁡(1)+sec⁡2(1)(x−1)L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x-1\right)L(x)=tan(1)+sec2(1)(x−1)﻿

﻿L(x)=tan⁡(1)+sec⁡2(1)L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)L(x)=tan(1)+sec2(1)﻿

﻿L(x)=tan⁡(1)+sec⁡2(1)(x+1)L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x+1\right)L(x)=tan(1)+sec2(1)(x+1)﻿

Incorrect

Great!

Determine the linear approximation of $f\left(x\right)=\sin\left(x\right)$ at a=0.

$L\left(x\right)=x$

$L\left(x\right)=-x$

$L\left(x\right)=0$

Determine the linear approximation of $f\left(x\right)=\sec\left(x\right)$ at a=0.

$L\left(x\right)=\sec\left(1\right)+\sec\left(1\right)\tan\left(1\right)\left(x-1\right)$

$L\left(x\right)=\sec\left(1\right)+\sec\left(1\right)\tan\left(1\right)$

$L\left(x\right)=\sec\left(1\right)$

Determine the linear approximation of $L\left(x\right)=\tan\left(x\right)$ at a=-1.

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x+1\right)$

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)$

$L\left(x\right)=\cos\left(1\right)$

$L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)\left(x-1\right)$

$L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)\left(x+1\right)$

Determine the linear approximation of $f\left(x\right)=\sin\left(x\right)$ at a=-1.

$L\left(x\right)=\sin1$

$L\left(x\right)=\sin\left(1\right)+\cos\left(1\right)\left(x+1\right)$

$L\left(x\right)=\sin\left(1\right)+\cos\left(1\right)$

$L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)\left(x+1\right)$

$L\left(x\right)=\cos\left(1\right)+\sin\left(1\right)$

$L\left(x\right)=\cos\left(1\right)$

Determine the linear approximation of $f\left(x\right)=\cot\left(x\right)$ at a=1.

$L\left(x\right)=\cot\left(1\right)-\csc^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\cot\left(1\right)+\csc^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\cot\left(1\right)+\csc^2\left(1\right)\left(x+1\right)$

Determine the linear approximation of $f\left(x\right)=\cot\left(x\right)$ at a=-1.

$L\left(x\right)=\cot\left(1\right)-\csc^2\left(1\right)\left(x+1\right)$

$L\left(x\right)=\cot\left(1\right)-\csc^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\cot\left(1\right)+\csc^2\left(1\right)\left(x-1\right)$

Determine the linear approximation of $f\left(x\right)=\sec\left(x\right)$ at a=0.

$L\left(x\right)=2$

$L\left(x\right)=1$

$L\left(x\right)=0$

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x-1\right)$

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)$

$L\left(x\right)=\tan\left(1\right)+\sec^2\left(1\right)\left(x+1\right)$