Questions

1 / 10

Time

Score

Linearization Of Exponential Functions

Determine the linear approximation of $f\left(x\right)=3^x$ at a=0.

$L\left(x\right)=\ln\left(3\right)x$

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

$L\left(x\right)=1+\ln\left(3\right)x$

Determine the linear approximation of at a=0.

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

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

$L\left(x\right)=3$

Determine the linear approximation of $f\left(x\right)=3^{\left(x+1\right)}$ at a=1.

$L\left(x\right)=9+9\ln\left(3\right)\left(x-1\right)$

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

$L\left(x\right)=6$

Determine the linear approximation of at a=0.

$L\left(x\right)=1+\ln\left(2\right)x$

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

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

Determine the linear approximation of at a=1.

$L\left(x\right)=3+2\ln\left(2\right)\left(x-1\right)$

$L\left(x\right)=3+2\ln\left(2\right)\left(x\right)$

$L\left(x\right)=3+\ln\left(2\right)\left(x-1\right)$

Determine the linear approximation of at a=0.

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

$L\left(x\right)=4+2\ln\left(2\right)x$

$L\left(x\right)=1+2\ln\left(2\right)x$

Determine the linear approximation of at a=-1.

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

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

$L\left(x\right)=\frac{1+\ln\left(2\right)x+\ln\left(2\right)}{2}$

Determine the linear approximation of $f\left(x\right)=3^x$ at a=1.

$L\left(x\right)=3+3\ln\left(3\right)\left(x-1\right)$

$L\left(x\right)=3x$

$L\left(x\right)=3\ln\left(x\right)$

Determine the linear approximation of at a=1.

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

$L\left(x\right)=4+\ln\left(2\right)\left(x-1\right)$

$L\left(x\right)=4+4\ln\left(2\right)\left(x-1\right)$

Determine the linear approximation of $f\left(x\right)=3^{\left(x+1\right)}$ at a=0.

$L\left(x\right)=3x$

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

$L\left(x\right)=3+3\ln\left(3\right)x$

Questions

Time

Score

Linearization Of Exponential Functions

Determine the linear approximation of ﻿f(x)=3xf\left(x\right)=3^xf(x)=3x﻿ at a=0.

﻿L(x)=ln⁡(3)xL\left(x\right)=\ln\left(3\right)xL(x)=ln(3)x﻿

﻿L(x)=1+ln⁡xL\left(x\right)=1+\ln xL(x)=1+lnx﻿

﻿L(x)=1+ln⁡(3)xL\left(x\right)=1+\ln\left(3\right)xL(x)=1+ln(3)x﻿

Determine the linear approximation of at a=0.

﻿L(x)=2L\left(x\right)=2L(x)=2﻿

﻿L(x)=2+ln⁡(2)xL\left(x\right)=2+\ln\left(2\right)xL(x)=2+ln(2)x﻿

﻿L(x)=3L\left(x\right)=3L(x)=3﻿

Determine the linear approximation of ﻿f(x)=3(x+1)f\left(x\right)=3^{\left(x+1\right)}f(x)=3(x+1)﻿ at a=1.

﻿L(x)=9+9ln⁡(3)(x−1)L\left(x\right)=9+9\ln\left(3\right)\left(x-1\right)L(x)=9+9ln(3)(x−1)﻿

﻿L(x)=1L\left(x\right)=1L(x)=1﻿

﻿L(x)=6L\left(x\right)=6L(x)=6﻿

Determine the linear approximation of at a=0.

﻿L(x)=1+ln⁡(2)xL\left(x\right)=1+\ln\left(2\right)xL(x)=1+ln(2)x﻿

﻿L(x)=ln⁡(2)xL\left(x\right)=\ln\left(2\right)xL(x)=ln(2)x﻿

﻿L(x)=1L\left(x\right)=1L(x)=1﻿

Determine the linear approximation of at a=1.

﻿L(x)=3+2ln⁡(2)(x−1)L\left(x\right)=3+2\ln\left(2\right)\left(x-1\right)L(x)=3+2ln(2)(x−1)﻿

﻿L(x)=3+2ln⁡(2)(x)L\left(x\right)=3+2\ln\left(2\right)\left(x\right)L(x)=3+2ln(2)(x)﻿

﻿L(x)=3+ln⁡(2)(x−1)L\left(x\right)=3+\ln\left(2\right)\left(x-1\right)L(x)=3+ln(2)(x−1)﻿

Determine the linear approximation of at a=0.

﻿L(x)=2+2ln⁡(2)xL\left(x\right)=2+2\ln\left(2\right)xL(x)=2+2ln(2)x﻿

﻿L(x)=4+2ln⁡(2)xL\left(x\right)=4+2\ln\left(2\right)xL(x)=4+2ln(2)x﻿

﻿L(x)=1+2ln⁡(2)xL\left(x\right)=1+2\ln\left(2\right)xL(x)=1+2ln(2)x﻿

Determine the linear approximation of at a=-1.

﻿L(x)=2L\left(x\right)=2L(x)=2﻿

﻿L(x)=1L\left(x\right)=1L(x)=1﻿

﻿L(x)=1+ln⁡(2)x+ln⁡(2)2L\left(x\right)=\frac{1+\ln\left(2\right)x+\ln\left(2\right)}{2}L(x)=21+ln(2)x+ln(2)​﻿

Determine the linear approximation of ﻿f(x)=3xf\left(x\right)=3^xf(x)=3x﻿ at a=1.

﻿L(x)=3+3ln⁡(3)(x−1)L\left(x\right)=3+3\ln\left(3\right)\left(x-1\right)L(x)=3+3ln(3)(x−1)﻿

﻿L(x)=3xL\left(x\right)=3xL(x)=3x﻿

﻿L(x)=3ln⁡(x)L\left(x\right)=3\ln\left(x\right)L(x)=3ln(x)﻿

Determine the linear approximation of at a=1.

﻿L(x)=x−1L\left(x\right)=x-1L(x)=x−1﻿

﻿L(x)=4+ln⁡(2)(x−1)L\left(x\right)=4+\ln\left(2\right)\left(x-1\right)L(x)=4+ln(2)(x−1)﻿

﻿L(x)=4+4ln⁡(2)(x−1)L\left(x\right)=4+4\ln\left(2\right)\left(x-1\right)L(x)=4+4ln(2)(x−1)﻿

Determine the linear approximation of ﻿f(x)=3(x+1)f\left(x\right)=3^{\left(x+1\right)}f(x)=3(x+1)﻿ at a=0.

﻿L(x)=3xL\left(x\right)=3xL(x)=3x﻿

﻿L(x)=ln⁡xL\left(x\right)=\ln xL(x)=lnx﻿

﻿L(x)=3+3ln⁡(3)xL\left(x\right)=3+3\ln\left(3\right)xL(x)=3+3ln(3)x﻿

Incorrect

Great!

Determine the linear approximation of $f\left(x\right)=3^x$ at a=0.

$L\left(x\right)=\ln\left(3\right)x$

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

$L\left(x\right)=1+\ln\left(3\right)x$

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

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

$L\left(x\right)=3$

Determine the linear approximation of $f\left(x\right)=3^{\left(x+1\right)}$ at a=1.

$L\left(x\right)=9+9\ln\left(3\right)\left(x-1\right)$

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

$L\left(x\right)=6$

$L\left(x\right)=1+\ln\left(2\right)x$

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

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

$L\left(x\right)=3+2\ln\left(2\right)\left(x-1\right)$

$L\left(x\right)=3+2\ln\left(2\right)\left(x\right)$

$L\left(x\right)=3+\ln\left(2\right)\left(x-1\right)$

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

$L\left(x\right)=4+2\ln\left(2\right)x$

$L\left(x\right)=1+2\ln\left(2\right)x$

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

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

$L\left(x\right)=\frac{1+\ln\left(2\right)x+\ln\left(2\right)}{2}$

Determine the linear approximation of $f\left(x\right)=3^x$ at a=1.

$L\left(x\right)=3+3\ln\left(3\right)\left(x-1\right)$

$L\left(x\right)=3x$

$L\left(x\right)=3\ln\left(x\right)$

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

$L\left(x\right)=4+\ln\left(2\right)\left(x-1\right)$

$L\left(x\right)=4+4\ln\left(2\right)\left(x-1\right)$

Determine the linear approximation of $f\left(x\right)=3^{\left(x+1\right)}$ at a=0.

$L\left(x\right)=3x$

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

$L\left(x\right)=3+3\ln\left(3\right)x$