The following statements are true EXCEPT A. lim x →2 x²=4 B. lim  x →-2 x=-2 C. lim x →-2 x³=8 D. lim x →-2 x⁴=-16

Q: ghing 16 pounds stretches a spring feet. The mass is initially released from rest from a point 2 fee...

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Q: The definite integral (-+) dx when evaluated is equal to - 11 Find the value of a." 12 3Vx. a

A: Given ∫49-xa+13xdx = -1112we know that∫xn dx = xn+1n+1 + C

Q: Find the value of k so that the value of S,"(2y – 1) dy is 10. 1 2 3 4

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Q: Examine the following functions for maxima-minima and trace the curves. a. Y = x* +1 a²x b. Y=- a²+x...

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Q: Given the equation y = exp(ax^(1/2)+b), which of the following plots will give you a straight line i...

A: Compare the equation with straight line equation.

Q: How many transformations must be applied to the graph of the function f(x) to get the graph of the f...

A: The transformation from f(x) to g(x)=2f(2-x)+2

Q: Step by Step Solve by Monges, given the partial differential equation  q2-2pqs+p2t=pt-qs,

A: This question is based on monge's method .....by the help of this method we got the desired solution...

Q: A. How do you define Differentiation? B. Explain the principle of derivative with a given function, ...

A: Differentiation 

Q: 8- 6- 4- 2. The graph of f(x) is shown in red. Draw the graph of g(x) = - f(x). -8 -7 -6 -4 -3 -2 Ma...

A: topic - graph of a function

Q: (:) 8. dw 4. 6tan w

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Q: P(#) Question 4: When working with rational functions of the form f (x) = and the function does inde...

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Q: For the function, find the following. X + 1 2x (a) f"(x) 242 (b) f"(3) = 2/3 ||

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Q: 1. Find the first derivative of the following. а. у%33x y = 3x² + 6 y = 2-1

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Q: Find all the second-order partial derivatives of the function f(x,y) = 4x2 + 9y + 7x2y?.

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Q: 20. Find the equation of the curve for which y" =x, and which passes through the point (1, 2) and th...

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Q: Suppose f(x) and g(x) are two functions such that: • f(3)=1 • g(3)=1 • f(3)=5 • g'(3)=7 What is (fg)...

A: we know that uv' = u'v+v'u                   product chain rule of differentiation

Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx b...

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Q: Solve the differential equation y' = e4Y sin(5x) and choose the correct answer from the following op...

A: Given:- y'=e4y sin(5x)  To find:- General solution of given differential equation

Q: 3 2 Suppose f(x) = 9x° + 7x? + 8. Which of the following are true? Select all that apply. OAs x → ∞,...

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: 14. Find the antiderivative of 5sinx In 5 cos x .

A: Follow the procedure given below.

Q: Identify the type of generalized integral +00 fx'e* dx- and in continuity (if converging) to be calc...

A: According to question,Given Integral,Let I= ∫0+∞ x2ex3 dx

Q: Since the start of the year, the price of gasoline has been decreasing at the cost of 5 cents per ga...

A: We  have given that the start of the year, the price of gasoline has been decreasing at the cost of ...

Q: J, 4. lim X-3 x2 - 9 x - 3 lim X3 x2 – 2x – 3 5. X - 3 lim X"i x2 – 2x – 3 6.

A: We need to find limit.

Q: 3. (D5- D-2D3 + 2D2 +D – 1)y = 0

A: This is a differential equation problem

Q: Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero betw...

A: We will use the intermediate value theorem. 

Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b. [...

A: Here we have to transformed the given integrand.

Q: Q2 Second-order non-homogeneous ordinary differential equation given as; y" + 3y' –10y = e2* Calcula...

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Q: 6. If f(x)dx = 5, f f)dx =2, and , f(x) dx = –1, find i f)dx. а. —2 b. 2 C. -3 d. 3

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Q: The rate of change in the profit (P) with respect to the number of units sold (x) is 0.0006x² + 10. ...

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Q: (x)

A: We will find the correct answer. 

Q: 2. (D2 + 3D)y = -18x: v = 0. Dy = 5 when x = 0

A: Given differential equation is  D2+3Dy=-18x  and the given conditions are y=0, Dy=5 when x=0 find th...

Q: 16x2 - 25 -da Evaluate the integral: 23 (A) Which trig substitution is correct for this integral? O ...

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Q: BThe distance from the point (-1, -2, 3) to the plane 2z = - 4x + 5 is [b] (input exact value in sim...

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Q: If f. g and h are functions defined on the set of real numbers defined by: F(x)= 3x+1, g(x) = 2x -1 ...

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Q: Question 8 ... (sin x – 1) dx + | (cos x + 1) dx = 4 C.) – 1 D.) - (1+) А.) —89 В.) —91 2 A A в) в D

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Q: 7= - + Cle2x general solution to the DE y"=2y+x Find C1 with the given condition y (1) =1/4

A: Given DE is y''=2y+xand the general solution is yx=-x3-14+C1e2xand given condition is y1=14find C1

Q: Consider the graph of f. y 4 3 1 1 2 2 3 4 5 6 7 8 9

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Q: a. Suppose f(x) = 17x* + 16x² + 6x – 13. Determine the degree of f. Preview b. Suppose g(x) = 7x³ De...

A: Topic = Polynomial   To find the degree of the polynomial, add up the exponents of each term and sel...

Q: | (3t + t*) sin(2t) dt 3.

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Q: If dx dy and y = 27 14 when x = 1, find y(2). %3D 3x-2

A: ∫x3x-2dx

Q: Find the value of k so that the value of f,"(2y – 1) dy is 10. 1 2 4 A) в B) c A D) D 3.

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Q: Find all the values of a such that the given series would converge. (– 1)"9"x" Σ n=1 (Vn+ 5) The ser...

A: Here we have to find the values of x such that the given series would converge.

Q: Test the series below for convergence using the ratio test. n2 Σ 1.5" n=1 The limit of the ratio tes...

A: f(n)=n2/1.5n

Q: Find the domain of the function. (Enter your answer using interval notation.) 3x3 - 2 f(x) = x2 + 3x...

A: Let's find. 

Q: Test the series below for convergence using the ratio test. n+ 2 24n +1 n=1 The limit of the ratio t...

A: Given: ∑n=1∞ n+224n+1where f(n)= n+224n+1Ratio test : l=limn→∞ an+1anif l<1 then the series is co...

Q: Find a parameterization for each of the following surfaces: (a) æ² + y² + z² – 4x – 6y = 12 (b) 2x² ...

A: We have to find the parametric representation of the following surfaces: x2+y2+z2-4x-6y=12       → ...

Q: if x < 0 if 0 < x < 1 -x² + 4x – 2 if 1 < x < 3 . Find lim f (x). if x 2 3 Given: f(x) = • %3D x-3 4...

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Q: P(z) how might the function 9(x) Question 3: When working with rational functions of the form f (x) ...

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Q: Find f, (X,y) and fy(x,y). Then, find fx(-3,1) and fy(-4, - 2). f(x,y) = - 2xy + 3y + 8

A: Given that: f(x, y)=-2xy+3y3+8

Q: (3 cos³ x-1 7. To evaluate dx, the integrand can be transformed to? 1-sin? x a. [(3cos³x+ csc²x)dx b...

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