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The document evaluates two expressions: 1) u(w(2)), where u(x)=x^2+3x+2 and w(x)=1/(x-1). It finds that u(w(2))=6. 2) w(u(-3)), where u(-3)=2. It then finds that w(u(-3))=1.
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The document discusses parabolas and their equations in real world contexts. It shows the steps to derive the equation of a parabola from its vertex: Y=1(X-2)^2+2. By expanding and simplifying this equation, the final equation is found to be Y=X^2-4X+6. This final equation is then compared to the actual equation derived from the parabola: Y=-0.083(x)^2+0.442(X)+1.544, showing their similarities.
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2. The chain rule is applied to find the derivative of two example functions, w = xy and w = xy + z, with respect to t along given paths for x, y, and z in terms of t.
3. The chain rule is generalized to the case of a function u of n variables, where each variable is a function of m other variables
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The document evaluates two expressions:
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2) w(u(-3)), where u(-3)=2. It then finds that w(u(-3))=1.
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The document evaluates two expressions:
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2. The chain rule is applied to find the derivative of two example functions, w = xy and w = xy + z, with respect to t along given paths for x, y, and z in terms of t.
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The document evaluates two expressions:
1) u(w(2)), where u(x)=x^2+3x+2 and w(x)=1/(x-1). It finds that u(w(2))=6.
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- AIM Global has been in business for over 45 years and is publicly traded on the NASDAQ and NYSE. It has over 700 product lines that are approved by regulatory bodies.
- The company emphasizes research and development, conducting clinical studies and using direct processing of plants from its own plantations.
- AIM Global measures the antioxidant levels in its products using the ORAC scale and produces supplements with high levels of antioxidants and other beneficial compounds.
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The document describes trends in CD and total revenue from 1990 to 2008. CD sales followed a quadratic function, peaking at 5000 in 1999 and declining to 0 by 2005. Ticket sales followed a linear function, declining from 1.5 to 0 from 1999 to 2005. Total revenue was modeled as a composite function of CD and ticket sales multiplied by 1.04 to the power of t, representing a 4% annual increase. When graphed from 1990 to 2008, total revenue increased until peaking around $24,000 from 2000 to 2001 before declining.
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The document evaluates two expressions:
1) u(w(2)), where u(x)=x^2+3x+2 and w(x)=1/(x-1). It finds that u(w(2))=6.
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- The company emphasizes research and development, conducting clinical studies with over 200 medical doctors and herbalists. It uses a direct processing method from plantation to careful harvest.
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The document evaluates two expressions:
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Example 2
- 1. Example 2 Let u(x)=x²+3x+2 and w(x)=1 x-1 a) Evaluate u(w(2)) b) Evaluate w(u(-3)) Method 1: Find u(w(x)) the sub into equation a) u(x) =x²+3x+2 u(w(x))=(1/(x-1))²+3(1/(x-1))+2 u(w(2))=(1/(2-1)²+3(1/(2-1))+2 =1²+3(1)+2 =6
- 2. Let u(x)=x²+3x+2 and w(x)=1 x-1 a) Evaluate u(w(2)) b) Evaluate w(u(-3)) Method 2: Find w(2) then sub into equation a) w(x)=1/(x-1) w(2)=1/(2-1) =1 u(w(2))=u(1) =1/(2-1) =6
- 3. Let u(x)=x²+3x+2 and w(x)=1 x-1 a) Evaluate u(w(2)) b) Evaluate w(u(-3)) Find u(-3) then sub into w(x) and evaluate b) u(x)=x²+3x+2 u(-3)=(-3)²+3(-3)+2 =2 w(u(-3))=w(2) =1/(2-1) =1