Find the Length of the Curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 7 }$

question 81

Multiple Choice

Find the length of the curve $\mathbf { r } ( t ) = 2 t \mathbf { i } + t ^ { 2 } \mathbf { j } + \ln t \mathbf { k } , 1 \leq t \leq e ^ { 7 }$
Select the correct answer.

• A) \(e ^ { 14 }\)
• B) \(e ^ { 14 } + 6\)
• C) \(e ^ { 7 }\)
• D) \(e ^ { 7 } + 6\)

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Definitions:

Distant Dendrite's Tree

The elaborate branching structure at the end of a neuron's axon, allowing for connections with other neurons.

Axon Hillock

The cone-shaped area of a neuron where the axon originates and action potentials begin.

EPSPs

Excitatory PostSynaptic Potentials (EPSPs) are changes in membrane potential that increase the likelihood of generating a postsynaptic action potential.

Axon Hillock

The cone-shaped area of a neuron where the cell body transitions to the axon, and from which action potentials are initiated.