Find an Equation of the Tangent Plane to the Surface

question 66

Multiple Choice

Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point. $$\overrightarrow { \mathbf { r } } ( u , v ) = ( 2 u + v ) \hat { \mathbf { i } } + ( u - v ) \hat { \mathbf { j } } + v \hat { \mathbf { k } } , ( 4 , - 4,4 )$$

• A) \(( x - 4 ) - 2 ( y + 4 ) - 3 ( z - 4 ) = 0\)
• B) \(2 ( x - 4 ) + 2 ( y + 4 ) - 3 ( z - 4 ) = 0\)
• C) \(z = 0\)
• D) \(( x - 4 ) - 2 ( y + 4 ) - 3 ( z - 4 ) = 0\).
• E) \(2 ( x - 4 ) - 2 ( y + 4 ) + 1 ( z - 4 ) = 0\).

Understand the characteristics and developmental challenges associated with autism spectrum disorder.

Explain the theories of Lev Vygotsky and his emphasis on social mentoring and language in cognitive development.

Recognize the importance of language and self-directed speech in cognitive development and problem-solving.

Describe the role of attachment and its impact on child development.

---

Definitions:

Injected Drugs

Medications that are administered through a needle directly into the body, bypassing the digestive system.

Prostate-specific Antigen

A protein produced by cells of the prostate gland, elevated levels of which can indicate prostate cancer or other prostate disorders.

Human Papilloma Virus

A group of viruses that can cause warts on the skin and mucous membranes, and in some cases, lead to cancers such as cervical cancer.

Venereal Disease Research Laboratory

A diagnostic test primarily used to detect syphilis through blood serum samples.