1. Determine the value for the number "a" so that lim x-2 3x² + ax + a +3 x²+x-6 will exist. Also determine the value of this limit. [TH/I-41

Q: Find an explicit solution of the given initial-value problem. dx - = 7(x²+1), x(77) = 1 - dt x = tan…

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Q: dN dt The rate of change of N is proportional to N. (Use k for the propor kN N(t) = Cekt Evaluate…

A: We are asked to find the value of N when t = 3

Q: Evaluate the integral fos√²²-1 f√²-1. 2x by first rewriting in the order dxdy. Enter the numerical…

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Q: A manufacturer can produce 4320 cell phones when a dollars is spent on labor and y dollars is spent…

A: Given that a manufacturer can produce 4320 cell phones when x dollars isspent on labor and y dollars…

Q: Find div F and curl F if F(x, y, z) = 10y³zºi – 8x³z¹ºj – 5xy³k. div F= curl F=

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Q: Give the Particular Solution of the following Differenti d²y dy dx2 +2. dx IBC: y(0) = 2 y'(0) = -2…

A: Topic:- differential equations

Q: Use the method of your choice to find the volume of the solid generated by revolving the region…

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Q: Find r(t) u(t). r(t) = (3-7)i + +³1+ j+ 4k u(t) = t²i - 8j + t³k r(t) u(t)= Is the result a…

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Q: Find both first partial derivatives. f(x, y) fx(x, y) = fy(x, y) = ху ,2 x + ,2

A: Find the partial derivatives

Q: Find div F and curl F if F(x, y, z) = 7evi-4 cos yj+ 10 sin² z k. div F= curl F

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

A: Here, the diameter of the hemisphere is 30 m. So, the radius of the hemisphere is: r=302=15m=1500 cm…

Q: 3. dy= 2x+y dx x+2y

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Q: An electronic games manufacturer producing a new product estimates the annual sales to be 4000…

A: According to given, Inoperative units= 1% Therefore, Operative units= 100-1 =99% =0.99

Q: Find the exact value of each of the remaining trigonometric functions of 0. 2 5 sin - and tan 00 cos…

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Q: Answer true or false. If f is not piecewise continuous on [0, ∞>), then L{f(t)} will not exist. O…

A: Topic:- application of integration    Definition :- A piecewise function is a function defined by…

Q: Find both first partial derivatives. h(x, y) = e(x¹0 + 10 hx(x, y) = h₂(x, y) =

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Q: If √√x + √√y = 8 and y(4) = 36, find y'(4) by implicit differentiation.

A: Given that x+y=8 and y4=36 we have to find y'(4)

Q: A power plant generates electricity over a twenty-four hour period. The number of megawatts, M, of…

A: Given  A power plant generates electricity over a twenty- four hour period the number of megawatts…

Q: 6).  State whether the series converges absolutely, conditionally, or not at all. ∞     n = 1 (−1)n…

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Q: Convert the given exponential function to the form indicated. Round all coefficients to four…

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Q: r = graph (8-2) i+ 10tj O It is a line in 2-space through the point (-2, 10) and parallel to the…

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Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2?

A: We have to find the lim inf and lim sup of sequence

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [(x + 3x²) dy

A: To evaluate: ∫C(x+3y2)dy...(1) where C is given by x=2t, y=4t⇒dy=4dt and 0≤t≤1

Q: Question 15 A box with a square base and no top is to have a volume of 4 cm³. Find the least amount…

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Q: D O 413 O 02 00 Question 5 04 Evaluate the limit limo tan(+h)-tan() h by recognizing it as a…

A: limh→0tanπ3+h-tanπ3h   The definition of the derivative of a function f(x) at x=a is given by:…

Q: Differentiate the function f(x) = 7√x - 2. (Use symbolic notation and fractions where needed.) f'(x)…

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Q: Sec-S 2 1 TanOLO

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Q: H.w: Find the LT of the following functions: 3-f(t) = cosh at cos at

A: Given, f(t)=cosh at cos at

Q: The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. Use linear…

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Q: Use the formula k(t) k(t) = "(t) || ||r' (t)||³ r(t) = 11 cos(3t)i + 11 sin(3t)j + 2tk ||r' (t) = to…

A: The given formula is; κt=r't×r''tr't3 And rt=11cos3ti+11sin3tj+2tk   As we know the Chain rule:…

Q: (Question # 5, 6, For the following exercises, find the local and absolute minima and maxima for the…

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Q: (Question #1, 2, 3, 4, f(x)=x²e* f(x)=et' inx f(x) = ln(4x³ + x) f(x)=In√√5x-7 1. 2. 3. 4. ror the…

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Q: a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Basic partial differentiation and integration is used

Q: or Questions 1-3, use the differential equation given by 1. Complete the table of values -1 X y dy…

A: Put value in function

Q: The function s(t) describes the motion of a particle along a line. s(t) = 14t-t² (a) Find the…

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Q: ll is thrown vertically upward from the top of a building (when t-Oseconds). It has a height functi…

A: Topic:- application of derivatives

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

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Q: -6 4 -2 19 6 4 2 2 6

A: The standard form of the equation of a hyperbola with center (h,k)(h,k) and transverse axis parallel…

Q: If f(x, y, z) = 1, then fff f(x, y, z)dV gives the volume of V.

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Q: 6. DETAILS ZILLDIFFEQMODAP11 4.5.045. Solve the given differential equation by undetermined…

A: To find out the solution of the differential equation by using the undetermined coefficients.

Q: A marketing specialist determines that when a certain product is released, the number of social…

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Q: Graph the level curves in the x-y plane the function f(x, y) = 2y- for z = -2,-1, 0, 1, and 2.

A: Given curve f(x,y)=2y-x23

Q: 2.) √ √9-4x² dx x² Solution: Case I let u = asino 2x = 3 sine x = 3 sino 2 dx = ² coso do 2 so, by…

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Q: Consider the following. W = xyz, X = S + 2t, y =s - 2t, z = st² (a) Find aw/as and aw/at by using…

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Q: A company that produces cell phones has a cost function of C = x² - 1200x+36,400, where C is cost in…

A: Derivate the cost function and equate it to zero to find the exact number of cell phones. Then again…

Q: Evaluate I C: arc on y = x³/2 from (0, 0) to (4, 8) (2x −y) dx + (x + 3y) dy.

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Q: etermine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that…

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Q: 32-2n Σ=3 Ln=3_25-n

A: We have to evaluate ∑n=3∞ 32-2n25-n.

Q: At which value does the function g(x)= 3x^4 - 4x^3 attain a minimum and what is the minimum value?.

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