9. If an object is dropped from a high cliff, then the distance (in feet) traveled after t seconds is given by the function d(t) = 16t?. %3D a. Find the difference quotient (average speed) over the interval [a, a +h]. Include units with your answer. b. Find the limit as h goes to zero of the difference quotient over the interval Ja, a + h|. Include units with your answer. What do you think this limit represent? 10. Given the equation: f(x) = -2x² + 5x – 1, find the equation of a line that passes through %3D a point on the graph where x = -1 and has a slope of -5.

Q: Find the focus and directrix of the parabola given by y2 = 12x. Then graph the parabola.

A: y2=12x Now comparing with y2=4ax, we get 4a=12⇒a=3 Therefore focus is, a, 0=3, 0 & directrix is,...

Q: The polynomial P(x) = 5x2(x − 2)3(x + 6) has degree.........  . It has zeros 0, 2, and......... The ...

A:

Q: Number 1   thank you!

A: Part (c): Given, limx→0+sin x ln x or limx→0+ ln x1sin x

Q: Answer the following

A: Given function fx=ex−1+2lnx+5x To find: f−16  

Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

Q: Find three positive numbers whose sum is 310 and whose product is a maximum. Step 1 Let the three nu...

A: To find three positive numbers whose sum is 310 and whose product is maximum, consider numbers are x...

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A: Answer(1): The graph of the given function fx is given. Since, the domain of the function is the col...

Q: Given an average cost function Cave=x^3−1/2x^2−e^0.5x, what is the correct form for the cost functio...

A: GivenCavg= x3-12x2-e0.5x

Q: (a) Either prove that ƒ is continuous at x = 3 or classify the type of discontinuity, with justifica...

A: " Since you have asked multiple question, we will solve the first question for you. If you want any ...

Q: Evaluate the integral. (Use C for the constant of integration.) 7 In(x) dx 4 + (In(x))?

A:

Q: Evaluate the double integral. 7x cos(y) dA, D is bounded by y = 0, y = x², x = 5

A: Given ∬7x cos y dydx , y=0 ,y=x2 , x =5

Q: a box with square ends of side x and a length L is to be made such that L+4x=4 meters. The dimension...

A:

Q: Determine whether the statement " If f is a function, then f(ax, ay) = a2f(x, y)" ,is true or false....

A: If f is a function, then f(ax, ay) = a2f(x, y).

Q: Evaluate the integral. (Use C for the constant of integration.) 11 tan“(x) sec (x) dx

A:

Q: Find all values of x such that fx>0 and all x such that fx<0

A: f(x)=-1x39-3 To find x values  such that f(x)>0 we find out x intercepts To find x intercepts , w...

Q: Solve the polynomial inequality and graph the solution set on a real number line. Express the soluti...

A:

Q: find the derivative of f(x) = cos(sin(4x+7)^4). simplify

A:

Q: f(x) = tan(x) and g(x) = 1 + sec(x). Find d/dx[f(x)/g(x)].

A:

Q: refer to y dx - 2x dy=(3y² - 2) dy. The differential equation can be rewritten as X' + p(y) x= q(y),...

A:

Q: A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. (a) Find t...

A: Given: Rate of change of volume of spherical balloon is dVdt=800cm3/min. (a) To find: Rate of change...

Q: Use the formula t = ln 2 /k that gives the time for a population with a growth rate k to double to s...

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: I need to find answers ?

A: (-9,0) is on the negative x-axis.  So the graph of option A only has (-9,0) on it.    Answer: A  

Q: Differentiate the function, and find the slope of the tangent line at the given value of the indepen...

A: f(x)=5x+3x,      x=1 We need to differentiate the function and to find the slope of the tangent at a...

Q: In the following exercises, use direct substitution to obtain an undefined expression.  (105) lim 2x...

A: The given limit expression limx→1-2x2+7x-4x2+x-2 Evaluate the limit bu putting x=1 =2×12+7×1-412+1-2...

Q: For the function, find the relative maxima, relative minima, and horizontal points of inflection. (I...

A: Given function is  y=13x3-x2+x+5 To find out relative maxima or minima , we take derivative y=13x3-x...

Q: Explain it correctly

A:

Q: Find the derivative.

A: Given,            f(x) = 5x4x + 1 + 2  

Q: O A total of $2,000 is invested at a simple interest rate of 7% for 5 months. How much interest is e...

A: Initial amount=P=2000 Interest rate=r=7%=0.07 Time=t=5 months=512 years I=interest earned=?   We wil...

Q: Suppose the graph of a function f is given to the right. Determine each of the following: a.) lim f(...

A: Given,        

Q: Find a value of n such that y = (x^n)(e^x) satisfies the equation xy' = (x-20)(y)

A:

Q: 3) If E={ students of a certain school },describe the complement of each of the following sets ( usi...

A:

Q: The revenue (in dollars) from the sale of x car seats for infants is given by the following function...

A: R(x)=24x-0.010x20≤x≤2400 To find average change in revenue apply formula Average=R(1050)-R(1000)1050...

Q: Find the Volume of the šólid generated by revolving the region bounded by the given lines and curves...

A: We know that volume of solid obtained by revolving the curve y=f(x) , x-axis, x=a and x=b about x-ax...

Q: Determine the equation of the line tagent to the function f(x)=x(5-x)4 at x=3   Please help me solve...

A:

Q: Determine whether the statement - "I can rewrite tan t as 1/cot t, as well assin t/cos t.", makes se...

A: yes, it does make sense.  as tan(t) is the inverse of cot(t)  

Q: One number is 7 less than a second number. Find a pair of such number that their product is as small...

A: We have to find two numbers in which one number is 7 less than a second number and product their num...

Q: Consider the function g(x) =- Which of the following statement(s) is/are true? x+3 L. lim g(x) does ...

A: Given function is, g(x)=x+cosxx+3

Q: Sketch the graph of a function f that satisfies all the following conditions: (i) f(x) > 0 for all x...

A: Definition used -                i) If f(x)>0 then graph is above x-axis .                ii) If ...

Q: Calculus Question

A: The given graph of f,

Q: 2. Find all values k that make this function continuous at x = 3. Зх — 9 - if x > 3 f(x) = x² – 3x 3...

A:

Q: Define the sine of t? Explain.

A: the function can be represented as:        

Q: number 3   thank you

A: Given: ∫2313−xdx To determine: The reason why the given integral is an improper Riemann integral. Wh...

Q: Solve sin(3x)cos(7æ) – cos(3x)sin(7x) - 0.2 for the smallest positive solution. X =

A: The value of x is 0.0503 

Q: Evaluate the integral. 8*V1-x² dx x³V

A: Let, z=1-x2dz=-2xdxdx=dz-2x When x=0, then z=1 When x=1, then z=0