Find the average rate of change of the function on the interval specified. g(x) = 6x3 − 7  on  [−3, 3]

Q: Which of the following is the normal line at the point (-1, 1, 1) to the surface 22 - 2y? - 35 - -4…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question.

Q: y=x² + 8x - 9 -intercept: (x, y) = -intercepts: (x, y) = (x, y) = (smaller x-value) (larger x-value)

A: Given query is to find x and y intercepts.

Q: Determine whether the vector field F is conservative. F(x, y, z) = ye²i + zexj + xe k conservative…

A: We have to check if F is conservative or not.

Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: e2+8i = a + ib, where: a = b i = i

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Q: Let f(x) be defined by Find f'(1). f(x) = (2x - 1).

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Q: Find curl(F x G) = V x (F x G). F(x, y, z)= i + 7xj + 6yk G(x, y, z) = xi - yj + zk

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Q: Exercise (a) Graph fand the secant lines passing through P(2, 4) and Q(x, f(x)) for x-values of 3,…

A: Here we have to evaluate the given function at given values of x

Q: Find the following limits (if they don't exist write DNE, ∞ or -∞ as appropriate): Answer: x-1 lim…

A: We need to find the limit limx→∞ x-12x2-7x

Q: Let v = (2, -1, 5) and u = (5, -7,3). Find 37 - 5u

A: We have to find 3v - 5u

Q: Answer got marked wrong, please fix it.

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Q: EX: Show that d² = 2πi where c is a unit § Z circle. C:1Z1 =1 Sol: ie Z= re io dzir e do 24 io ixe…

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Q: x=2x+1 y -2 4 3 2 > 2

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Q: 2. A person invests $2,125 in an account earning 9% per year compounded continuously. How much will…

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Q: The count in a bacteria culture was 300 after 15 minutes and 1500 after 40 minu count grows…

A: We will solve.

Q: 25. Find equations of all lines having slope −1 that are tangent to the curve y 1/(x − 1). = 1/4…

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Q: □ on show that f(x)= 3x is inte the integralble definition. I043 uning [0,4]

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Q: Identify the surface y − 3 = x² +.

A: Solution: Given data, y - 3 = x2 + z2

Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

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Q: Consider the equation below. 2 3 — 15 os(0) - (a) Find the eccentricity. = (b) Identify the conic. O…

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Q: Evaluate the function at the given values of the independent variables. Simplify the results. f(x,…

A: Topic = Functions

Q: Convert the point (√3, 1, 0) from Cartesian to spherical coordinates.

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Q: Find the general solution of the following differential equation. y"+11y12y = 0 NOTE: Use c, and ce…

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Q: Determine whether the equality is always true -10√x-9 (x-9)² f(x, y)d ydx = ₁ + f(x, y)dx dy. ²+9…

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Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: 3. Find the sum of the series 2 3 5 6 1 π 1 7 1 (-)-(3) - 2 (² + 1 (3) - () -- () - () +- ... 2! 3…

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Q: Take the derivative of  (x+y)3=3x-4y+5 with respect to the variable t . Do not rearrange and move…

A: NOTE: Refresh your page if you can't see any equations. . take derivative on both sides with…

Q: Find an equation for the graph above.

A: NOTE: Refresh your page if you can't see any equations. .

Q: For the differential equation y(n) + P₁(t)y(n-¹)+...+Pn(t)y=0 with solutions Yı, •, yn Abel's…

A: We have to find the Wronskian of a fundamental set of solutions of the differential equation.

Q: need

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Q: Assume that the radius r of the cylinder below is decreasing at a rate of 2 m/s, and that its height…

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Q: Calculate the Taylor series for 1/x about 1. O 1+ (x + 1)(x-1) ²+ (x+1) ³-... ○1-(x-1) + (x − 1) ²—…

A: We know Taylor series expansion of 1/(1+x) is given by, 1/(1+x)= (1+x)-1= 1-x+x²-x³+x⁴-....

Q: 0 T 2 T 2 f² sin(x - y) dxdy is eg elect one: True False

A: Topic:- application of integration  Yes given statement is true .

Q: Əw Find Ət using the appropriate Chain Rule for w = x² + y² + z² where x = 10rsin(s), y = 10tcos(s),…

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Q: If f(x) = = f'(x) = 3x (sin x + cos x), find f'(x). Evaluate the derivative at x = 4. Enter an…

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Q: If a company spends r million dollars on research, it sales will be s million dollars, where r and s…

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Q: g'(x) = Find the derivative of the function g(x) = e² 52+3

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Q: Find a linear equation that expresses the relationship between the temperature in degrees Celsius C…

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Q: Find curl(curl F) = x (V x F). F(x, y, z) = 4x³yzi + yj + 4zk

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Q: Find the interval of convergence of the power series .x" /n². 0-1<x<1 0-1<x< 1 0-1≤x≤1 O-1<x< 1

A: The given power series is xn/n2.

Q: Consider the following. y 4 3 Find its foci. 2 1 -1 -2 Find an equation of the ellipse. smaller…

A: we need to find the equation for ellipse

Q: Question 19 -6 -5 -4 -3 -2 구 -2 244 1 + -2 -3 -6- -7 k(w) Find an equation for the graph above.…

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Q: If F = Pi+Qj+ Rk, prove that div (curl F) = 0

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

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Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find f'(1). Note: Your answer (if it's not an integer)…

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Q: The answer for x is correct but the answer for dy is wrong.

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Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: The position of a particle moving in a straight line is given by s(t) = e-*cos(5t) for > 0, where…

A: We have to find the necessary equation that must be satisfied.

Q: For function f(x, y) = 5- | 2 E find the maximum value of the directional derivative at (3, 2).

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Q: Express the number –2 in the form R(cos(0) + i sin(0)) = Re where R> 0 and 0 ≤ 0 ≤ 2π. NOTE: Enter…

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