mits Assignment 1 Find the domain and range of the function. Use interval notation to write your result. a. f(x)=x3 b. f(x)=√3x-2 c. f(x)=4-x² d. f(x)=(x-2) Assignment 2 Evaluate the function at the specified values of the independent variable. Simplify the result. (1) f(x)=3x-2 (a) f(0) (b) f(x-1) (c) f(x+6x) (2) f(x)=x-4x+1 (a) f(-1) (b) f(c+2) (c) f(x+dx) Lin Yinhe Mathematics and Modern Life 2240 2 mits Graphs, and Li Assignment 3 Femur Length Anthropologists can estimate a person's height from the length of certain bones. The height h (in inches) of an adult human female can be modeled by the function h(1)=1.95/+28.7, 15<24, where / is the length (in inches) of the femur, or thigh bone. (a) Find the domain and range of the function. (b) Suppose a female's femur was 16 inches long. About how tall was she? (c) If an anthropologist estimates a female's height to be 5 feet 10 inches, about how long was her femur? one-to-one 1 fox)=3x-2 √(x-4)=3(x+11 +(x+5)=3( Lin Yinhe Mathematics and Modern Life

Q: Use the shortcut rules to mentally calculate the derivative of the given function. f(x) = 2x-1…

A: Step 1: Step 2: Step 3: Step 4:

Q: 12. For the function f(x) = ax³ + bx² – 5x + 9, determine the values of a and b so that f(−1) = 12…

A:

Q: Use algebra and the properties of limits as needed to find the given limit. If the limit does not…

A:

Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: The linear approximation of a functionf(x) at a point a is given by the equation:…

Q: Suppose that y = f(x) is a particular solution to the differential equation condition f(2) = 3. A.…

A:

Q: List the points in the graph in the interval -1 <x<7 at which the function is not differentiable.

A: If a function is not continuous at x=a, then it is not differentiable at x=a.

Q: Find the derivative of the function. s=t² In |t| ds dt

A:

Q: Select which one of the following statements is true for the function f(x) = 5x²+2x+3. 1 The…

A:

Q: Solve the initial value problem y' = 7y² sin x, y(0) = 7. y =

A:

Q: Solve the initial value problem d= (x-7)(y — 9), y(0) = 6. - y =

A:

Q: Suppose that the function f(x) is defined as f(x) = 2 sin²x-9 sin x cos x + cos² (2x) — 7 sin(2x)…

A: The given function

Q: 20 Σ 24 1822 i=1 8 + 323 4 - 3r² + 15 5 12

A:

Q: 10. Sally reasoned that if she drove 30 km/hr in one direction over a 180 km distance, and then…

A: Approach to solving the question: Detailed explanation: Examples: Key references:

Q: Find the magnitude and direction (in degrees) of the vector u = Round to the nearest tenths place. =…

A: The magnitude of vector ∣∣u∣∣=8.1The direction of vector is θ=119.7∘

Q: Use the definition of Taylor series to find the first three nonzero terms of the Taylor serie f(x) =…

A: By using the definition of Taylor series to find the first three nonzero termsof the Taylor series.

Q: Find the average rate of change for the following function. f(x)=5x³-3x²+2 between x = -2 and x = 3…

A: The formula for the average rate of change is: Average rate of change=b−af(b)−f(a)​ Where: a is the…

Q: Find the linear approximation to the following function at the given point 2 f(x)=-3x-4x; a = 3

A: GivenThe function and the value of a=3.The expression for the linear approximation is given byTo…

Q: Find the average rate of change for the following function. 2 f(x)=5x³-3x² + 2 between x = -2 and x…

A:

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 450…

A: Step 1:Step 2:Step 3:Step 4:

Q: Evaluate. (√2) 4+ log2√3

A: Step 1: (2​)(4+log2​3​)=(2​)(4+log2log3​​)=5.2642

Q: 8) Suppose you are at the point (2, 1, 82) on the hill given by f(x,y) = 100-4x²-2y (where the z…

A: The objective of this question is to understand the concept of directional derivatives and gradient…

Q: (3) Find all critical points of f(x,y) = -x³+3x+13-31² and classify each as yielding local max.,…

A: Critical points: (-1,0),(-1,2),(1,0),(1,2)Saddle points: (-1,0),(1,2)Relative maximum:(1,0)Relative…

Q: Assume that the cost, in thousands of dollars, of airing x television commercials during a sports…

A: a.) Marginal cost function is the first derivative of the given cost function. Then,     Cost: C(x)…

Q: show all steps please! thank you!

A: The slope of the tangent line at point (x,y) is given as

Q: et-1 t-07+2te-2t-7et Given that lim [7427][h(r)]] = = = 3 use the Rules of Limits and 28 -…

A: Given: limt→0​[[7+2tet−2t−7etet−1​][h(t)]]=−283​ Step 1: Simplify the expression inside the…

Q: Calculate the monthly finance charge for the credit card transaction. Assume that it takes 10 days…

A: The objective of this question is to calculate the monthly finance charge for a credit card…

Q: Find all local extrema using the second derivative test. 1. f(x)=x2-1n(x) 2. f(x)=x-2sin(x) 3 .…

A: Second Derivative Test Formula:If f′′(c)&gt;0, then f(x) has a local minimum at x=c.If  f′′(c)&lt;0,…

Q: Use the product rule to find the derivative of the function. (Hint: Write the quantity as a…

A: Approach to solving the question:Please see attached photos for detailed solutions. Thank you.…

Q: Let аз +-(633) A and suppose that det A = 8. Determine det B if b3 B = a15c1a2+5c2 a3 +5c3 -3c1 -3c2…

A:

Q: Please solve the following calc 3 problem (show all work by hand plz)

A: Step 1:Step 2:

Q: Suppose a sample of a certain substance decayed to 65.6% of its original amount after 300 days.…

A: Step 1:​(a) To find the half-life of the substance, we will use the formula for exponential…

Q: The limit L of an alternating series that satisfies the conditions of the Alternating Series Test…

A: Step 1:Step 2:

Q: Write an equation for the function graphed below.

A:

Q: 2. Area of a circle: Consider the polar equation r = 2Rsine. Sketch the graph and note the limits…

A:

Q: Find the derivative of the function. y= log 5√√7x+8 7 dx 2(In 5)(7x+8) O A. A. dy О в. B. dy 7 In 5…

A:

Q: Consider the points A(2,3,7), B(0,3,3), and C(5,2,-4). Find a) The largest angle in triangle Abc…

A:

Q: Find a power series for the function, centered at c. f(x) = =1 Σ 1 f(x) C = 2 5 - x' n = 0 Determine…

A:

Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1 + 5y², 1 ≤…

A: If you have any questions let me know in comment box thankyou.

Q: Use the graph of the function f to find lim f(x) and lim f(x). X-00 ∞ - <x Select the correct choice…

A: • As x approaches negative infinity, the graph of the function f(x) approaches the line y = 3.…

Q: Find the linear approximation to the following function at the given point a. f(x)=3x-1; a= -2 L(x)=…

A:

Q: Q3 please

A: Step 1:

Q: Use the quotient rule to find the derivative of the given function. 2 8t² -5t f(t)= 9t +2 f'(t) = ☐

A:

Q: When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C…

A:

Q: Find the particular solution of the differential equation that satisfies the initial condition(s) f"…

A: To find the particular solution of the differential equation that satifiesthe following initial…

Q: Consider the given limits (a is a constant, f(x) > 0). lim f (x) = 0 xa limp (x) = ∞ xa lim g(x) = 0…

A:

Q: x3 14. Find the point(s) of the tangent to the curve h(x) = = - 5x28x+3 with same slope 4 3 as 48x +…

A: Step 1:Step 2:Step 3: Step 4:  Thanks

Q: 7. Given: sin(x)= ½, sin(y)= ½ and 0<x,y< π <? find the value of the following 2 expression:…

A: Step 1: Step 2: Step 3:

Q: Find the indicated derivative for the function. f'(x) for f(x)=2x-4x+4x-4 f''(x) = ☐

A:

Q: dx² dx 543-5+ y = 0; y(0) = 4y'(0) = 0

A: To solv the following initial value problem.