Determine the equation of the line through the point P tan) that is parallel to the line with equation 5x -8y +4.5 0. %3D

Q: Differentiate y = (x² + 7x – 1)(5x + 2)

A: We have to differentiate y with respect to y

Q: find the equation of the tangent line and normal line to the ff. curves at the indicated point.

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Q: The base of a 10-ft ladder leaning against a wall begins to slide away from the wall. At the instant...

A: Given:          From the above figure     dxdt=6 ft/sec

Q: 5 -3 Example: Let a = -2 a2 -13 and b 8 |. Is b in Span {a,, az}? %3D 3 -3 1

A:

Q: Se sin 3x dx Using integration by parts, if u = sin 3x and dv = e*dx , %3D what should be du and v? ...

A: We know that, The expression for the integration by parts: ∫udv=u·v-∫vdu   Given: I=∫exsin3xdx

Q: 5. Consider the graph of y = f(x) below. On the same set of axes sketch a clearly labelled graph of ...

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Q: Find the equations of normal of the curve y = 2x- x'at (2, 0). a. 2x +y = 4 b. 2x - y = 2 O C. X- 2y...

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: Find the MacLaurin series of f(x) = sinh(3x) . Express your answer in the form Σan (x - c)^n. The pr...

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Q: market analyst working for a small-appliance manufacturer finds that if the firm produces and sells ...

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Q: A spherical balloon is inflating with helium at a rate of 64x ft / min. How fast is the balloon's ra...

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Q: Use integration by parts to evaluate the integral: 5t2e-6t dt = %3D

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Q: Sin x 10. y = 2+Cos x 3 2+Cos x Ob. (2+Cos x)? Cos x C. (1+Cos x)2 1+2 Cos x d. (2+Cos x)? Oa. (2+Co...

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Q: Suppose f (x, y) = 1æ² + 2ry– 3y, P = (1,-3), and u = (, 8). %3D 20 20 A. Compute the gradient of f....

A: function f(x,y)=x2+2xy-3y2

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the tri...

A: Given that the altitude of a triangle is increasing at a rate of 3 centimeter/ mimute.⇒dhdt=3 centim...

Q: Let f be the function given by f (x) = sin(2x) cos(1 +x). What is the average value of fon the close...

A: Given function f(x)=sin(2x) cos(1+x)       ; 1≤x≤3 use the formula 2 sin A cos B = sin(A+B)+sin(A-B)

Q: Let f be a differentiable function such that f (3) = 2.345 and f' (x) = ln(x² + 1). What is the valu...

A: solution:-f'(x)=ln(x2+1)f(x)=∫ln(x2+1) dxusing integration by partsf(x)=∫1·ln(x2+1) dx=ln(x2+1)∫1 dx...

Q: n of the coefficient/s when we evaluate (sec(x) - tan(x))²dx

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Q: Calculate the integral: dx J (e² – 4)(e* + 6)

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Q: MY NOTES ASK YO Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementa...

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,...

A: Given: I=∫-∞122x-32dx   We know that the power rule: ∫xndx=xn+1n+1+C ; n≠-1 And ∫c·fxdx=c·∫fxdx

Q: sin²(x) + sin(x) To evaluate the xp- using basic formula of integration (without using cos (x) subst...

A: ∫sin2x+sinxcos2xdx  

Q: Assume that a is an angle in standard position whose terminal side contains the point (15, 8). Find ...

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Q: y = x- Sin 2x %3D

A: topic - derivative of a function

Q: xy' = y elw) – x

A:

Q: Find all the values of x where the graph of f(x) = 2x³-36x2 + 192x 9 has a horizontal tangent line. ...

A: topic - derivative of a function and point of horizontal tangent line

Q: Consider the parabola given by y = x² + 1. a) Use Lagrange's method to find the point on the parabol...

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Q: n-1 9. Given the series - 8 n=1 Does this series converge or diverge? O converges O diverges If the ...

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Q: Find the derivatives c %3D b)' y = e(4*+) c) y = e*(sin x %3D d) y = In(3xe-> %3D

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Q: Show that f(x, y) = e2x cos(x + In y) satisfies the differential equation 2f - yfyx = 5f.

A: Given that fx,y=e2xcosx+lnyShow that 2fx-yfyx=5f

Q: Solve the given differential equation. x?y" – 3xy' – 7y = 0 y(x) = %3D ,x > 0

A: Given differential equation x2y''-3xy'-7y=0

Q: 222 Compute the work done for a force F=12/x N from x=1 to x=2 m.

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Q: Find the tangent line to the curve y = 2x - x? at (2,0)

A: We can find the required answer as below

Q: Let f be the function given by f (x) = | (-t² + 2t + 3) d't. On what intervals is f 10 increasing?

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

Q: 4x4 + 3 dx = 4x5 + 15x +2 1 + C 5(4x5+15x+2)² A) ++3x .5 + C 15 - x²+2x 2 (C In 4x + 15x+ 2+ C D) 5 ...

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Q: V1-x? 1 x2 + 1 1 X.

A: Follow the procedure given below.

Q: Find the intervals where the function y=f(x)y=f(x), whose graph is given below, is increasing and wh...

A: from the given graph

Q: Use implicit differentiation to find the derivative of: 9. х2 +x Arctany %3D у + 4 (2x+Arctany)(1+y²...

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Q: A pump allows water to flow into a pool at the rate of r (t) = 2t liters per minute, where t is the ...

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Q: Е. 46.-50 Given the function g and asked to estimate lim g(z), three students created tables. Each t...

A: The person A has used the most closest values of x to 0. So, it is the best approach because we can ...

Q: D. Tell if the function is continuous at given interval. 31-35 f(x) = ; 2.x +4 [-2,2]

A: Given, f(x)=x2/(2x+4)

Q: Let f (x) and 8(x) be antiderivative of h (x), The which of the following is true? (A None of the gi...

A: Note: If f(x) is anti- derivative of h(x) then  f'(x)=h(x) . Just use this definition and find that ...

Q: 3x° - 5xe* + 2xcos(x) Evaluate: (A x3 - 5ex + 2sin(x) + C 3x4 B. - 5ex + 2sin(x) + C 4 C) None of th...

A: Given query is to eveluate the integral.

Q: 1. Find all possible points of discontinuity and classify each discontinuity as removable, jump esse...

A: This is a limit and discontinuity problem

Q: 19. State the limit definition of the derivative and use it to compute the following derivatives: d....

A: Find your answer below 

Q: 5. The depth of water in a port is modelled by the function d(t) = pcosqt + 7.5, for 0 <t < 12, wher...

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Q: Find the indicated trigonometric value in the specified quadrant. Function Quadrant Trigonometric Va...

A: Given query is to find the value of sin function.

Q: 6. Evaluate the limits 10r – 2x4 + r3 + x² lim 4r1 + x² + x+1 5g2020 + 76 14r³ + 2 lim I-00 T2021 + ...

A: 1. limx→∞ 10x-2x4+x3+x24x4+x2+x+1

Q: SOve the inequality x²34-10 LO X-4 using the test-point method. Express your answer in interlai nota...

A: x2-3x-10x-4&lt;0⇒x+2x-5x-4&lt;0⇒x&lt;-2  or   4&lt;x&lt;5⇒Solution:  x&lt;-2  or   4&lt;x&lt;5  Inte...

Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope -12 at x = -1, and p...

A: To find a parabola with equation.