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Q: find the unique solution of the second-orderinitial value problem. y" + 6y' + 5y = 0, y(0) = 0, y'(0...

A: Given: y''+6y'+5y=0y(0)=0y'(0)=3

Q: Find (E) (f+g) (-2)= (F) (fg)(1)= (F)(f-g)(2)=

A: Given, f(x)=-x3+3x+4 g(x)=-5x-6

Q: (a) g(x) = f(x) – 5 -2 -1 1 2 1 f'(x) -1 -2 -5 3 3 g'(x)

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st ques...

Q: Find the limit. lim sin(5x) 6x

A: Given: limx→0sin5x6x

Q: Identify the intervals where f (x) = + - 8-x? – 16 - 16 -x is increasing and decreasing on the inter...

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Q: The cost (in dollars) of producing x units of a certaIH COn (a) Find the average rate of change of C...

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Q: Which of the following functions are continuous for all real numbers x? 1 y I. II. y = 2* III. y = s...

A: y=1x does not at x=0. Because 10 is undefined.y=2x this function exists for all real values of x. y=...

Q: Use the definition of continuity to determine whether the shown is continuous at a = 2.

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Q: A quadratic function f is given. f(x) = x2 − 4x (a) Express f in standard form. f(x) = ...

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Q: Which one is the formula for the arc-length function of a smooth curve r(t) for t>a. ||r" (u)|| du T...

A: Given smooth curve rt for t≥a

Q: Select the statement that is false about the difference quotient. The difference quotient can be...

A: Given: The difference quotient can be represented by f(x+h)−f(x)/(x+h)−x or f(x+h)−f(x)/h The diffe...

Q: Suppose that the dollar cost of producing x appliances is c(x)=1300+90x−0.3x2. a. Find the average...

A: Given c(x)=1300+90x−0.3x2 is cost of producing x appliances.

Q: Use the Intermediate Value Theorem to show thatthere is a root of the given equation in the specifie...

A: Given expression is sinx=x2-x for 1,2 Simplifying further ,we get x2-x-sinx=0 As we know that polyno...

Q: A piecewise function is given (attached). Use properties of limit to find the indicated shown limit,...

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Q: Write an equation for a rational function with: Vertical asymptotes at z = 6 and a 1 a intercepts at...

A: Given that the vertical asymptotes are x=-6 and x=1 So the denominator is (x+6)(x-1). x-intercepts...

Q: The function g(C)=1.8C+32 takes a temperature in degrees Celsius, C, and outputs the corresponding t...

A: Given that: The function g(C) = 1.8 C + 32. The function g(C) takes a temperature in degrees Celsi...

Q: 3. The Squeeze Theorem states that if f(x) < g(x) < h(x) when r is near a and lim f(x) = L = lim h(a...

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Q: The profit of a company, in dollars, is the difference between the company's revenue and cost. The c...

A: Definition used - Profit = Revenue -cost P(x) =R(...

Q: Equations are given whose graphs encloses a region. Find the area of the region. ( Give an exact ans...

A: Given that : The function: f(x) = 32x g(x) = - x - 12

Q: Consider the vector functionrit)-(1, 2t, t"), Find the unit tangent vector T(t) when t

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Q: Use the product rule to find the simplest answer￼

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Q: A force of 8 lb is required to hold a spring stretched 8 in. beyond its natural length. How much wor...

A: Given: A force 8 lb is required to hold a spring stretched 8 in. beyond its natural length.

Q: Find the entire domain on which the function f is one-to-one and non-decreasing. Write the domain in...

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Q: Differentiate the following and simplify the answer to the simplest form￼

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Q: Find equations of the tangent line and normal line to the given curve at the specified point. y = 8x...

A: Given data: The given expression for the curve is y=8xex. The given point is (x1,y1)=(0,0). The ...

Q: 4. Find the arc length of function y = x2+ x- 2, -2 SXS1

A: Given: y=f(x)=x2+x-2 and -2≤x≤1 We have to find the arc length of the functionf(x).

Q: Differentiate. f(x) = x2 sin(x) f'(x) =

A: The function is fx=x2sinx.

Q: Given the functions f (a) = -a2 +3x +4 and g (x) = -5x- 6. find (go f) (2)=- (Use ^ for exponents, f...

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Q: question 52 please

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Q: Let h(x)=f(x)g(x). If f(x)=4x^2−4x+4,g(−1)=2, and g′(−1)=0, what is h′(−1)? Do not include "h′(−1)="...

A: Given, h(x)=f(x)g(x), f(x)=4x2−4x+4, g(−1)=2 and g′(−1)=0 f(-1) = 4-4+4 = 4 f'(x) = 8x-4 ∴ f'(-1)= ...

Q: Plz show work

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Q: Differentiate the following and simplify the answer to the simplest form￼

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Q: Please help me I don’t understand

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Q: Solve the following IVP using Laplace Transform. (i) y′′−4y′=e^(3t), y(0)=0, y′(0)=0 (ii) y′′+3y′+2y...

A: given Initial Value Problem is, (i) y′′−4y′=e^(3t), y(0)=0, y′(0)=0 (ii) y′′+3y′+2y=e^(-t), y(0)=0 y...

Q: A cylinder has a height equal to its radius. Find the rate of change of volume V with respect to rad...

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is in...

A: Ratio test: Let an be a sequence of positive real numbers and limn→∞an+1an=l then 1. The series ∑n=1...

Q: (a) P(q)=3q^2+q+7 Find the derivative by using the definition. p'(q)= (b) Find the instantaneous rat...

A: P(q)=3q^2+q+7 We need to find the following (a) Find the derivative by using the definition. p'(q)= ...

Q: Find the derivative of the trigonometric function. y = sin((πx)6)

A: Here given Function as y=sinπx6

Q: Calculate the area enclosed between y sin? (x) and sin (x) on the interval = 0 <x<T.

A: The area A of the region bounded between two curves is A=∫x1x2fx-gxdx Given fx=sin2xgx=sin3x and x1=...

Q: Find the slope of the graph of the function at the given point. f(x) = 5 cos...

A: According to the question, we have to find the slope of function fx=5 cosx-9x at the point 0,5. The ...

Q: Evaluate the integral. (Use C for the constant of integration.) 5x+e5z te* dx

A: Given, ∫6e5x + e5x dx

Q: Solve the given initial-value problem. (x + y)2 dx + (2xy + x2 − 3) dy = 0, y(1) = 1

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Q: Identify the surface with equation 9x2 – 4y?+ 16z2 – 144 = 0.

A: Given: The equation 9x2-4y2+16z2-144=0 To find: The name of type of surface with the given equation.

Q: Solve and graph the solution set on a number line: 3x + 1 > 7x - 15.

A: According to the question, we have to solve inequality 3x+1>7x-15. Many simple inequalities can b...