Given the Vector-Valued Function Below, Evaluate $$\mathbf { r } ( 11 + \Delta t ) - \mathbf { r } ( 11 )$$

Multiple Choice

Given the vector-valued function below, evaluate $$\mathbf { r } ( 11 + \Delta t ) - \mathbf { r } ( 11 )$$ $$\mathbf { r } ( t ) = \ln t \mathbf { i } + \frac { 8 } { t } \mathbf { j } + 4 t \mathbf { k }$$

A) $\ln \left( 1 + \frac { \Delta t } { 11 } \right) \mathbf { i } - \frac { 8 \Delta t } { ( 11 + \Delta t ) 11 } \mathbf { j } + 4 \mathbf { k }$
B) $\ln \left( 1 + \frac { \Delta t } { 11 } \right) \mathbf { i } + \frac { 8 \Delta t } { ( 11 + \Delta t ) 11 } \mathbf { j } + 4 \Delta t \mathbf { k }$
C) $\ln \left( 1 + \frac { \Delta t } { 11 } \right) \mathbf { i } - \frac { 8 \Delta t } { ( 11 + \Delta t ) 11 } \mathbf { j } + 4 \Delta t \mathbf { k }$
D) $\ln \left( 1 + \frac { \Delta t } { 11 } \right) \mathbf { i } - \frac { 8 \Delta t } { ( 11 + \Delta t ) } \mathbf { j } + 4 \Delta t \mathbf { k }$
E) $\ln \left( 1 - \frac { \Delta t } { 11 } \right) \mathbf { i } - \frac { 8 \Delta t } { ( 11 + \Delta t ) 11 } \mathbf { j } + 4 \Delta t \mathbf { k }$