ati sis 57-58 Determine whether f'(0) exists. 2 loel 1 x sin if x + 0 57. f(x) = if x = 0 10

Q: tind the Point an the graph of the given function at which the slope of the tangent line is the give...

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Q: q2.1 Evaluate the following limits.

A: Given limx→-22x4-8x+16 =2(-2)4-8(-2)+16=2(16)+16+16=32+32=64

Q: 1. Use the limit definition to find f'(x) for f (x) =

A: The limit definition of derivative is given by, f'x=limh→0fx+h-fxh here fx=1xfx+h=1x+h  

Q: what is the FV of the investment. Round  to nearest cent. $7,000 for 4 years at 4.75%  annual intere...

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Q: A pharmacist wants to establish an optimal inventory policy for a new antibiotic that requires refri...

A: Given:Total packages =2400ordering cost =$12carrying cost =$4  

Q: The function of f(x)=2.75x^2

A: Here f(x)=2.75x2x is length of the book.Length of books is normally between 4-12 inches.⇒4≤x≤12

Q: From the book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications by DENNIS G. ZILL...

A: Given, the function f(t) = e-t sint, we have to find the Laplace of this function.

Q: Evaluate the integral. '5 x - 4 dx x2 - 3x - 18

A: We first factor the denominator. ∫-25x-4x2-3x-18dx=∫-25x-4(x-6)(x+3)dx

Q: 6) find the domain and range of the following piecewise function in the graph below (3,4) (5,3) 1.0 ...

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Q: Airport B is 300 mi from airport A at a bearing N 50° E (see the figure). A pilot wishing to fly fro...

A: The line AC=3560×150=87.5mi

Q: (6.1,6.2) Expand the following expressions as much as you can: (a) ez+In(3)-z

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Q: For the following exercises, use the functions y=f(x)y=f(x) to find df/dx at x = a and x = f − 1(y)...

A: Given: (a). y=f(x)(b). f(x)=6x-1, x=-2 To Find: 1. dfdx at x=a.2. x=f-1y3. df-1dy at y=fa

Q: The temperature of a sample of a fluid that is being heated in a laboratory is given by h(t) = 30t −...

A: The rate of increase in temperature of a sample of a fluid is given by ht=30t-t2 degree Celsius, whe...

Q: I need help better understanding of Calculus Exponential Growth and Decay and Related Rates.  For in...

A: Given Data: The equation of continuously compounded interest is: At=A0e0.08t   For the money became ...

Q: Please help, thank you so much!

A: Population grows at the rate proportional to the population. In year 2000, population is 6115 millio...

Q: Find the difference quotient of​ f; that​ is, find f(x+h)−f(x)/h, h≠0, for the following function....

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Q: q3.2 Find the following limits analytically or state that they do not exist.

A: Given that limx→8-1x-8. Note that the value of the function y=1x-8 approaches -∞ as the value x appr...

Q: If we let u = then du x2 dx, and so we have x3 cod cos(u)|| COS dx = du.

A: Answer in the box is  -1/2π.

Q: The question is attached

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Q: For each of the following exercises, decompose each function in the form y=f(u) and u=g(x), and fin...

A: Given y=-6sin-3x To decompose the function in the form y=f(u) and u=g(x) Here    y=-6sinx-3 u have...

Q: q3.5 Find the following limits analytically or state that they do not exist.

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Q: Evaluate the integral. (Use C for the constant of integration.) 13 dx Vx + xVx

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Q: Find an equation of the line through the given pair of points. (-7,-1) and (-4,-9)

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Q: Find the indicated side x. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assum...

A: In the given triangle ABC, , length of side AC is 3 and  ∠A=34o, ∠C=85o Since, sum of angles of a tr...

Q: 1) Determine whether the equation defines y as a function of x. y2=3-x2   2) Find the domain of the ...

A: NOTE We’ll answer the first question since the exact one wasn’t specified. Please submit a new quest...

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞  ...

A: The given limit of expression is lim x→∞+5x2+5x-42x2-3x Divide the expression by highest denominator...

Q: Find the volume of the solid obtained when the region under the curve y = xV4-x2,0 < x < 2 is rotate...

A: The volume of solid revolution V=∫abπfx2-gx2dx fx=x4-x2 where, a=0 and b=2

Q: Evaluate the integral. (Use C for the constant of integration.) 11 dx x²V 4x² - 1

A: Given integral ∫11dxx24x2-1=11∫dxx24x2-1 Now consider ∫dxx24x2-1 Use substitution method to solve th...

Q: Identify the quadric surface with equation a² +9y² – z = 0. O elliptic paraboloid O hyperbolic parab...

A: The given equation -x2+9y2-z=0 The quadric surface of above equation is "hyperbolic paraboloid" Proo...

Q: At 9:00AM , a thermometer reading 70 ∘ Fis taken outdoors where the temperature is 15 ∘ F. At 9:05AM...

A: Given that, A thermometer reading  70°F is taken outdoors where the temperature is 15°F at the time ...

Q: question below

A: Since you have asked  multiple questions in single request  so we  will be answering only first ques...

Q: ク2 X ty +Z=

A: n1→=324       n2→=111n1→×n2→ = 324× 111    (using cross product)           b  =-211

Q: Question: Evaluate the following. Va + 4+h – Væ +4 lim h -4Va + 4 Va + 4 +4 1 2Va +4

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Q: If an object is dropped from a 192-foot-high building, its position (in feet above the ground) is gi...

A: Given data:   The height of the building is h=192 feet. The given expression for the position of the...

Q: For each of the following functions, find (f−1)′(a). 271) f(x) = x − (2 / x), x &lt; 0 ,a = 1

A: The given function  fx=x-2x To find f-1 y=x-2xx2-2x=yx2-yx-2=0x=y±y2+82

Q: find the derivative.

A: ddxuv=vdudx+udvdxHere u= 1+4x5, v=3+x-x28dudx=51+4x4×4  ,   dvdx=83+x-x27×-3x2g'x=3+x-x28  5 1+4x4 4...

Q: Locate the stationary points of the following functions and categorise them using second order infor...

A: z=f(x,y)=xey-2y+x22-3x..........(1)

Q: There exists a field that is populated with a large amount of sunflowers. The amount given in time t...

A: We are given the amount of the population of sunflowers, in terms of t (in months): The given functi...

Q: The region under the curve y = tan? x from 0 to T/4 is rotated about the x-axis. Find the volume of ...

A: Given data: *The equation of the curve is y=tan2x *The curve is rotated from 0 to π4 about the x axi...

Q: The question is attached

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Q: Two​ functions, f and​ g, are related by the equation g(x)=f(x−2). Use the numerical representation ...

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Q: For the following exercises, find dy/dx for each function. 228.  y=(3x^2+3x−1)^4

A: The given function y=3x2+3x-14 Differentiate both sideds with respect to x using chain rule dydx=d3x...

Q: A rectangular page is to contain 64 square inches of print. The page has to have a 4-inch margin on ...

A: Area of the page =64 inches square; To find the dimensions: Let width be  (y+2) inches considering t...

Q: A sum of $15,000 was invested in two municipal bonds, which pay 7% and 9% simple interest. The annua...

A: Let money invested at 7% interest rate = x Money invested at 9% interest rate = y Simple interest at...

Q: Transform the following summation by making the change of variable j = i- 6. When i = 7, then j = So...

A: Given:j=i-6

Q: f(x), a. find the slope of the tangent line to its inverse function f-1 at the indicated For the giv...

A: a)The slope of  y=f-1x is     y'=1f'f-1x given fx=2-3+x2f'x=2×-1x2-32×2x       =-4xx2-32  

Q: I can't figure out the second portion of this question highlighted in red. Can you help me find the ...

A: Your answer is correct but it's your mistake change the variable in the place of 'x' we take variabl...