implify the difference quotient by rationalizing the numerator. Vz - 8 - Vz 8 ead more about Topic 15: Rationalizing the numerator or denominator

Q: A ball is thrown downward with a speed of 11 ft/s from the top of a 121-foot-tall building. After t ...

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Q: If s(t) = 4t3 – 6ť² – 24t + 8, represent the position of a particle traveling along a horizontal lin...

A: Let's find. 

Q: Solve the following equation; domain 0osx < 360°; 3 cot x + V3 = 0 O 120 240 60 300

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Q: Find the derivative of y = (4 - 2x³)(2x + x³). O a. y= 12x5+ 16x - 12x² - 8 O b. y = 12x° + 16x³ + 1...

A: As per our guidelines we are supposed to solve only one question i.e. the first one. For the solutio...

Q: Find the solution to the initial-value problem. dy dx = y2ex sin(2x), y(0) = 1 y =

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Q: Identify the most appropriate differentiation rules to be used in finding the derivative of the foll...

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Q: Identify the most appropriate differentiation rules to be used in finding the derivative of the foll...

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Q: The position of a hummingbird flying along a straight line in t seconds is given by s (t) = 3t – 10t...

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Q: theorem/ het f ,9EDCI) ; Xo E I, Then O iP xER t Xo then f is differentia ble a and f +g is difteren...

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Q: (a) Calculate the limit lim (z,y)→(0,0) x³ + y*' or show that it does not exist.

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: If s(t) = 10t – 15t2 – 60t + 5, represent the position of a particle traveling along a horizontal li...

A: The given position function is st=10t3-15t2-60t+5. The velocity function vt is the first derivative ...

Q: cos(a

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Q: Solve: y" + 6y' + 9y = cos(3x) 1. Find yc 2. Find yp 3. General Solution

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Q: Assume the following: lim f(r) = 3 lim g(x) = = 12, and lim h(x) = -3. %3D Compute the following lim...

A: The given limits,limx→cf(x)=34, limx→cg(x)=12 and limx→ch(x)=-3

Q: 2. Find the slope of the tangent line to f(x)=V4-V+5 at the point where x 4.

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Q: cln /3 2e" Ve2a + 1 dx

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Q: In Exercises 5–10, find an equation for the tangent line to the curve at the given point. Then sketc...

A: Given query is to find the equation of the tangent at given point.

Q: Lou and Jacob each sold 200 pieces of jewelry.  If 20% of Lou's sales were rings, and Jacob sold 35 ...

A: Given lou and jacob each sold 200 pieces of jewelry. 20%of lou and 35 ring of jacob.

Q: The position of a hummingbird flying along a straight line in t seconds is given by s(t) = 4 – 11t m...

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Q: Consider the integral -7 dx If the integral is divergent, type an upper-case "D". Otherwise, evaluat...

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Q: Find the indicated derivative and simplify. 4x -6 y' for y = 2 + 2x y' = D %3D

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Q: a Identify the inproper intergrals an ex plain (briefly) why it is improper () e 5 dX D x-ス ーメー2

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Q: 1. Create a Probability Distribution Table for: a) a Sum when 2 Dice are rolled. You list a table of...

A: A) a Sum when 2 dices are rolled.  Sum  Probability 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36...

Q: A rocket is fired vertically upward from the ground. The distance s in feet that the rocket travels ...

A: Solution is here

Q: Solve the system of simultaneous equations using Gauss-Jordan method 20x1 - 9x2 + 15x3 = 354 - - 9x1...

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Q: rocket is fired vertically upward from the ground. The distance s in feet that the rocket travels fr...

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Q: For the curve 16x° = y?(12 – x) complete the following. a. Find equations of all lines tangent to th...

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Q: 3) Find an equation of the plane which contains the points P(-1,2,1), Q(1, –2, 1) and R(1,1, –1).

A: Equation of a plane passing through 3 points P(x1,y1), Q(x2,y2) and R(x3,y3) is given by, x-x1y-y1z-...

Q: A ball is thrown downward with a speed of 15 ft/s from the top of a 225-foot-tal building. After t s...

A: This is application of derivative problem

Q: Consider the following. dt 49 + t2 Let t = 7 tan(0) and determine the following. %3D dt d0 t = 0 → 0...

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Q: Does the following system have a unique solution? Explain. ​2x – 3y + z – 1 = 0 ​Y – z – 2 = 0 ​X...

A: Cramers rule

Q: 2x + 10 dx x² (x – 4) Evaluate

A: I = 2∫(x+5)x2(x-4) dxperforming partial factorization;(x+5)x2(x-4)=Ax+Bx2+C(x-4) (x+5) =A x(x-4)+B(x...

Q: Given the graph of g(x) on the right: -10- Apply the following transformations below using a transfo...

A: Required formulas: Reflection about the y-axis is : x, y → -x, y. Horizontal stretch by 2 is: x, y ...

Q: 3.(Straightforward) Verify that the piecewise defined function { x*, x 0 y = is a solution of the d...

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Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few t...

A: Reciprocal of given sequence in in Arithmetic Progression(AP). So, write nth term of AP and then tak...

Q: 3) Determine the value(s) of k that make the functionf (x) continuous for all x. Show your work for ...

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Q: Find the coordinates of the point on the graph of y = x^2− x + 3 at which the tangent is parallel to...

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Q: Slopes, Tangents, and Normals In Exercises 31–40, verify that the given point is on the curve and fi...

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Q: Evaluate the instantaneous rate of change: (Please solve using Limits only) A spherical balloon is ...

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Q: Consider the integral -4 dx x2 If the integral is divergent, type an upper-case "D". Otherwise, eval...

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Q: = - 13, e is in the third quadrant, and x is in the fourth quadrant; evaluate tan 29 24/5 24/7 12/13

A: Here we will find tan2θ,

Q: 1-lim r. In r Answer =1/2

A: note: as per our company guidelines we are supposed to answer only one question. Kindly post other q...

Q: ((2x-y²)´ (x,y) # (0,0) Let f(x, y) = x2+y4 2, (x, y) = (0,0) Is f continuous at (0,0)? Do fr(0,0) a...

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Q: cln /3 2e" Ve2 + 1 dx

A: The integration of the integral is 2ex√(e2x+1) limit from 0 to ln√3.

Q: Determine the limits of the following using the table of values. 4. lim vx3 - x x-2 5. lim x-0 x+1 x...

A: Please refer to the image below

Q: Second Derivatives Find y" in Exercises 59–64. 62. y = 9 tan (3)

A: y=9tanx3Differentiate w.r.t.xy'=ddx9tanx3y'=9ddxtanx3y'=9sec2x3ddxx3y'=9sec2x313y'=93sec2x3y'=3sec2x...

Q: The graph of a polynomial function is given. What is the smallest degree that the polynomial could h...

A: The given graph is:   What is the smallest degree that the polynomial function could have?

Q: A rocket is fired vertically upward from the ground. The distance s in feet that the rocket travels ...

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Q: Differentiating Implicitly Use implicit differentiation to find dy/dx in Exercises 1–14. 6. (3xy + 7...

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Q: What are the types of discontinuity? describe each

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