Find an equation of the tangent line to the curve at the given point. у %3 бех + х, (0, 6)

Q: Solve the system by the substitution method.   3x−y = 21 x+8y = 7

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Q: Find an equation of the tangent line to the graph of y = g(x) at x = 6 if g(6) = -5 and g'(6) = 3. (...

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the functi...

Q: Evaluate the integral f 2x (x² + 5) dx using the substitution 13 u = x +5. 2x (x² + 5)*° d =| +C

A: I =∫ 2 x (x2+5)13 dx  u = x2+5du = 2x dxI =∫ u13  du We know that,∫ xn  dx =xn+1n+1+C

Q: 3 V1+x³ [6] S dx > x-2

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Q: 2/3 if fox)= 3x- point A(8,2) to B (27,17) l0, find the length of the graph of f frome

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Q: solve for nonbermagnenous difleemrial equation.

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Q: 3x lim The limit 2 x-2 (see graph) is

A: Here, to find the given limit: limx→2+3xx-2

Q: Find torsion of the motion r(t) = . Leave your answer correct to two decimal places.

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Q: 2. Given the functions below, find A. (A + B + C + D+ E+ F) B. (P + Q+R+ M + N) (x² + 1)(x +1) y = 2...

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) xV7 - x2 dx

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Q: [2x+5y=7 3x + 2y = -6' 1. Solve the linear system using graphical method.

A: The given linear system,2x+5y=73x+2y=-6

Q: ax²ª (x2a+1)°dx

A: Given,           ∫ax2ax2a+13xdx

Q: Find the volume of the solid generated when the region enclosed by y=x^3, x=1, and y=0 is revolved a...

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Q: 23. What is dx? 3 – e4r e2z + V3 In e2r + V3 In |e2x а. +C C. +C 2 e2x – V3 V3 /3. b. V3 +C V3 +C 2x...

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Q: Using integration bby parts, uV-/v du. Txt +2x+ 2 cove for solution. dv = V =

A: According to the question, we will choose u and v to solve this question by integration by parts .

Q: olve a nonlinear equation by making a change of the dependent var portant such equation has the form...

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Q: Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that ...

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Q: Items 15 The graph of a function f is shown. On top of the graph of f, sketch the graph of f'. Use a...

A: The graph of the functions are given as 

Q: 18. Determine the antiderivative of f(x) = 3e2"csch(e2"). a. coth(e2") + C 3 coth(e²") + C с. 2 3 3 ...

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Q: Question 3 Evaluate dt A 313-1+C B 12-1+C c) 312-t+C D 312– 31+ C

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Q: 2. Let b 1, and graph C ate- using different values for a. Explain the effect of the parameter a.

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Q: Use the Integral Test to determine whether the infinite series EL is convergent. (Use symbolic notat...

A: Here, the given series is: ∑n=1∞19n2+1 Using the Integral Test, to determine the series is convergen...

Q: sech(In x) dx J-5

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Q: dx V4x – x2

A: Given function, It can be solved by converting denominator Into (x-2)2 form Then by substituting  u=...

Q: Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable ...

A: We have to solve this given bernouli equation. 

Q: Suppose that the amount in grams of a radioactive substance present at time t (in years) is given by...

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Q: Find the angle, 0, that is cotermimal with 20T where 0 < 0 < 2T. Find the angle, 0, that is cotermim...

A: Coterminal Angles are angles  both have same initial side and terminal sides. To get coterminal angl...

Q: dy Write down a differential equation of the form dt = ay + b whose all other solutions diverge from...

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Q: 25. n- (1+) n = 1 M 8

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Q: Estimate the slope of a line tangent to the curve f(x) = -2x2 + 3x +5 at point P(1, f(1))by doing th...

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Q: dx x2 (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb in...

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Q: Use technology to evaluate the given expression. Take 1.6 7.3 1.4 -2.39 5.1 A = and B = 5.5 0 44.8 1...

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Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(6y) dy = 0, ...

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Q: The following graph shows the rate of change n(t) of the number of active eBay users, in millions of...

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Q: Evaluate the following limits. (b) lim v9r² – 5x + 3x

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Q: .2 1 0, Jo 0/ a² +y? + z2 fipxpzp?

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Q: 27. w = ry + yz+ za, x=r cos 0, y=r sin 0, z = r0; dw dw when r = 2, 0 = 1/2 dr' de

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Q: Find the equation of the tangent line of y = 4e* at xo = 0. (Use symbolic notation and fractions whe...

A: y=4exSubstitute x=0y=4e0=4The point is (0,4)

Q: A tank in the shape of an inverted right circular cone is full of water. The water weighs 62.4 pound...

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Q: 2 SET UP AN INIELLAL foRmULA fer Tte VOLume uf THE ScaO 2 C-ÉNELATEN UHEN THE RACIION BOUDEO BY Y=x,...

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Q: Find the Maclaurin polynomials of orders n = 0, 1, 2, 3, and 4 and then find the nth Maclaurin polyn...

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Q: Convert the point (1, , V3) from cylindrical to spherical coordinates. A. (2. 5. 5) 4' 6 В. 2,

A: To convert cylindrical coordinates (r, θ, z) to spherical coordinates ( ρ, θ, φ) we use following fo...

Q: All edges of a cube are expanding at a rate of 6 centimeters per minute. Draw an accurate  picture t...

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Q: Let f(x) = 5x + 20x². Then the equation of the tangent line to the graph of f(x) at the point (2, 90...

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Q: Let f be a function defined on the closed interval -4sxs4. The graph of f', the derivative of f, is ...

A: Let's find. 

Q: Given the: 7(t) = (cos (3t), 4t, sin (3t)) Find the folowing: show complete solution a. unit tangent...

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Q: Find the derivative of y(x) = In (9(ln(x))’). (Use symbolic notation and fractions where needed.) dy...

A: To find the derivative of yx=ln9lnx7.  

Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to...

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Q: S(x+ )´ dx 2 1 X X.

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Q: ax ve

A: To evaluate: I=∫dxex...(1)