X+2 At what points is the function y = continuous? 2 X- 9x + 14 ... Describe the set of x-values where the function is continuous, using interval nota (Simplify your answer. Type your answer in interval notation.)

Q: dy 2 + y = 0, y(0) = -3 dt

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: e-2x 2+x In 3x csc' x -) f(x)=. b)Use logarithm to differentiate: y = (3х-1)

A: a)f(x)=ln(3x)csc2x-x5e-x3f(x)=sin2x. ln(3x)-x5e-x3differentiating w.r.t…

Q: п! n4 n=1

A: The given series is: ∑n=1∞n!n4 Let, an=n!n4; n≥1

Q: Consider the function f(x): - 4x + 6x - 8. f(x) has a critical point at x A. Find the value of A: A…

A: For critical points ofa function we first find the derivative of the function and equate it to zero.

Q: o<×くT ② Foのコ 2 [:

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Q: Please help

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Q: 4. Use L'Hopital's rule to evaluate lim(1 – 2 sinh(r))ach(=).

A: 4) To evaluate: limx→0(1-2sinh(x))csch(x)  which is in 1∞ form.

Q: Product A and Product B are two different items manufactured by the same firm. Product A is…

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Q: Find the solution of y' = 2(2x-y) which passes through the point (0, -1) the answer should be y=2x-1

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Q: Verify Green's Theorem by evaluating both integrals ам y? dx + x2 dy dA ay for the given path. C:…

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Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: A ferris wheel is 50 meters in diameter and boarded from a platform that is 5 meters above the…

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Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

A: Given query is to find the equation of the tangent.

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. e2x –…

A: Solve the exponential equation algebraically.

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

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Q: 7. 1 (x dy – y dx) = 0 %3D x² + y²

A: Here, the given DE is: 1x2+y2(x dy -y dx)=0...(1)

Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: Find div F and curl F if F(x, y, z) = 6e#Y i – 7 cos yj+ 9 sin² z k. div F= curl F=

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Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: -945° is equal to i radians. (Type your answer in this format: a*pi/b where a and b are integers.)

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Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

A: Solving the problem by finding the value of integration.

Q: Find the S(x* +) dx xe-1 А. 1x? + c e-1 4e xe+1 В. Ix2 + c e+1 2e xe+1 С. 1x3 + c e-1 Зе xe+1 1 D.…

A: Given query is to find the derivative of the expression.

Q: Find the equation of the tangent plane to the graph of f(x, v) = In (17x² – 14y²) %3D at the point…

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Q: Use the One-to-One Property to solve the equation for x. 3x - 1 = 27 %3D X =

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Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: Evaluate lim (x)/

A: We can find the  limit as below.

Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 3 r(t) = e"i+ etj 9ts K(t) ||

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Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: Find the e v

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Q: 86. If f'(x) > 0 for all real numbers x and s(1) đt = 0, which of the following could be a table of…

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Q: For the function f(x)=2x^{2}+4x-1f(x)=2x2+4x−1, find the slope of the secant line between x=-1x=−1…

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Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

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Q: Find V × (V × F) if F(x, y, z) = 4xyj+2xyz k. V × (V × F) :

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Q: Find the length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: cos x e) f(x)= e* х

A: Topic = Derivative

Q: xdy + (y – cos x)dx = 0, y (- = %3D

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Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

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Q: Evaluate the indefinite integral: .3 dx x² – 2x + 5

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Q: (a) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) =…

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Q: In the year 2000, the population of a small city was 43,000. The population grows at a rate of r(t)…

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Q: ||r(t) × r"(t)|| Use the formula k(t) : to find «(t). %3D r(t) = e"i+e-tj K(t):

A: K(t)=?

Q: Find div F and curl F if F(x,y, z) = xzºi+ 5y°x²j+ 5z?yk.

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Q: The graphs of the function f (r) = 7- a and g(a) = 3 are given below. %3D 10 8 f(x) = 7-x2 4- g(x) =…

A: topic- area bounded by curves

Q: a) f(x) =(5x + 3)(7x² - 2) using the product rule b) f(x) = (3x? - 5) using the chain rule c) f(x) =…

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Q: For the curve given by r(t) = (5 sin(t), –2t, – 5 cos(t)), Find the unit tangent T(t) = (| Find the…

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Q: Evaluate the given integral by changing to polar coordinates.     sin(x2 + y2) dA   R, where R is…

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Q: S (In 2x2 dx

A: Evaluate the integral :    ∫ln 2x2 dx

Q: 6. Consider the DERIVATIVE f' graphed below. Sketch a possible graph of the original function f on…

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Q: x2 dx (x+2)3 In |x + 2| + 4x+6 4x+6 (ar+2)a +C In |x + 2| – (x+2)= Option 1 Option 2 희im lx + 2 +…

A: Given problem:-

Q: Evaluate the line integral, where C is the given space curve. xyeY dy, C: x = 3t, y = 2t, z 4t,…

A: Here we have to find line integral.