Find \( div \ {\bf F} \) where                                    \( {\bf F}= \langle x-y+z^{88}, -y-cos(e^{7x}), z+\tan(xy^{6}+1). \rangle \)

 Evaluate \( \int_{C} yz \ \mathrm{ d}s \) where \( C \) is the line segment from \( (1,0,0)\) to \( (1,3,4)\). 

Let \( {\bf F}=\langle y^{3}-1, 3xy^{2}+\frac{1}{y} \rangle\). Find \( \int_{C} {\bf F} \cdot {\bf dr}\) if \(C\) is the curve defined by \({\bf r}(t)=\langle \sin^{3}(t), e^{t} \rangle\) where \(0 \leq t \leq \pi\). Hint: The curve is NOT a closed path. Use FTLI.

Calculate \( \int_{C} {\bf F} \cdot {\bf dr} \) where \( {\bf F}= \langle 2xy, x^{2}+3y^{2} \rangle\) and \(C\) given by                                                 \( {\bf r}(t)= (\ln (t^{3}+1) \sin(t)) {\bf i} + (\cos(t) t ){\bf j},\) where \(0\leq t \leq \pi\).

a) Compute the curl of \( {\bf F} = e^{x}yz \ {\bf i} + 2 e ^{x}yz^{2} \ {\bf j} + e^{x}y^{2}z^{2} \ {\bf k}\), and thereby deduce that \({\bf F} \) is not conservative. b) Show \({\bf G} = y^{2}z^{3} \ {\bf i} + 2xyz^{3} \ {\bf j} + 3xy^{2}z^{2} \ {\bf k} \) is conservative by finding an explicit potential function \( \phi \), so that \( {\bf G} = \nabla \phi\).

Cognitive (Knowledge) I.C Anatomy & Physiology 8. Identify common pathology related to each body system including:  a. signs b. symptoms  c. etiology Question:  List the signs and symptoms of myocardial infarction. What are some  causes of this condition?

Cognitive (Knowledge) I.C Anatomy & Physiology 8. Identify common pathology related to each body system including:  a. signs b. symptoms  c. etiologyQuestion:  List the signs and symptoms of diabetes mellitus. What are some causes of this condition?

Cognitive (Knowledge) I.C Anatomy & Physiology  5. Identify the anatomical location of major organs in each body system Question: The brain is located in the peripheral nervous system.

Cognitive (Knowledge) I.C Anatomy & Physiology  5. Identify the anatomical location of major organs in each body system Question: The cervix is in the lower part of the uterus.

Cognitive (Knowledge) I.C Anatomy & Physiology 7. Describe the normal function of each body system Question:  Which of the following is not a function of the respiratory system?