The gradient at any point (x, y) of a curve is given by dy-3x² +ax-36 where a is a constant. The curve passes through the points (1, -7) and (3,-5) Find the equation of the curve..

Q: 15 S A B (c) D (x+1)dx (x+2)(x-1)² 1 2 -- 9 1 2 " 9 3 -lo 1 9 " - - W|N 2 1 9 3 W|N 3 -S[₂ = A B +…

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Q: - e*) sinh x + e* cosh x + ex In the indefinite Integral in(cosh x + ex). A In(cosh x + e*)- sinh x…

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Q: πT Evaluate the integral: sin(3x)cos(3x) dx រ 1 A 3 (B) i D 1 براس 1

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Q: Evaluate the double integral: A 40 B 80 C 60 30 ²(3x² +9y²) dxdy

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Q: 1. Let f{x«y} = v/r? + y? oa a) Find Ꭷf of Để ông Ꭷf of of Ꭷf Ꭷx2 0x0y` Ꭷyòx' dy2 b) Find 2. Find an…

A: We are allow to solve one question at a time . If you need rest of answers please upload it…

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Q: Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed…

A: fix cost $200 20 item cost $400 here per item cost = 400/20 = $20 cost function  C(x) = 200 + 20x…

Q: S Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, the limits of…

A: limit of integration

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Q: If g(x) == [e'-In(2t+1)]dt, find g''(x) . dx A ex-In(2x+1) 4 B (2x+1)² 4 (2x + 1)² 2 D (2x + 1)²

A: Here given that: g(x)=ddx∫-1xet-ln(2t-1)dt Using the Fundamental Theorem of Calculus: g(x)=ex-ln…

Q: Given A (В B [²₁f(x) dx = 0 and 11 6 11 5 55 6 √ √ ² f(x) dx = 11 6 0 evaluate 0 [²3f(x) dx - ₁2f(x)…

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Q: - 1₁₂ (3+√4-2²³) dx -2

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Q: 1 X + X Solve the integral: Gin|5+x²|+C A 5 @ B {/in/1+x³²|+c C © =√³ m/₁ + x ²³ / + C 6 ©…

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Q: If g(x) = - [e' - In(2t+1)]dt, find g''(x) . dx A e* -In(2x+1) 4 B (2x + 1)² 4 C (2x + 1)² 2 D (2x +…

A: To solve the following problem

Q: f(x) = Jax+b (2x²-1 if x < 2 if2 ≤ x

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Q: antiderivatives does a function of the form f(x)=x" have when n*O? may vary depending on n How many…

A: Formula: Antiderivative of xn = xn+1/n+1

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Q: Evaluate the double integral: 2 √² √ (3x² +9y²) dxdy A 40 B 30 C 60 D 80

A: Double Integration by iteration:

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

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Q: 1 √√√√√x + x S Solve the integral: 5 @ =³√√/1+ x ³²³/ + C A {m/1+x²³² |+c ==ınlı 5 6 B C ©…

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Q: Determine the integral: x²cosxdx (A) x²sinx+2xcosx-2sinx + C (B) x²sinx-2xcosx+2sinx + C…

A: topic- indefinite integral

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Q: Solve

A: We have to calculate the given indefinite integral

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A: Topic:- application of integration

Q: Which of the following can be determined given f(x) dx = 5₁ x) dx = 5,₁ ₁ g(x)dx=7, and h(x) dx = -5

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

A: Solution: Natural length  = 3 ft   ---&gt; 18 ft-lb 3 ft to 6 ft

Q: Question 17 The improper integral A 00 B) e C) 0 (D) 1 if the 0 edx is

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Q: - EXAMPLE 3 Find the particular solution of 3xy' y = lnx + 1, satisfying y(1) = -2. x > 0,

A: It is a first order differential equation.

Q: 5 Let f(x) = 5x + 3x²³² + 1 and g(x) = 3x²+2x+1 in 27 [X]. Determine the quotient and remainder upon…

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Q: - States √1+1² * tanx V1+t2 0 1+e' 1+tan²x 1+ e tanx In (secx) √ 1+tan²x 1+ e tanx If f (x) = A B…

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Q: How many antiderivatives does a function of the form f(x)=x" have when n*0₂ (A) 1 (B) none may vary…

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Q: Let f(x)=√3x-2 on the interval axis and find the volume of the resulting solid. 43л -unit 3 135 83…

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Q: dx (x+1) log(x+1) ¹__In[10g(x+1)]+ C In 10 - - log² (x+1)+C 2 -In10 log² (x+1)+C 2 In 10…

A: On solving this we will get Option (D) is correct

Q: ion 8 apply General Power Formula of Integration on which of the following sinhucothudu cosha coshu…

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A: We have to find the next approximate newton rapson formulae.

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1₁ 3 A 2/2 unit² А 3 B -unit²…

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Q: Question 13 3 2 Evaluate the triple integral: f(x+y+z)dydxdz A) 24 B) 18 C) 6 D) 12

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Q: What is the range of the function y = 5 sin(0+ 60°) - 4? O -60° ≤ y ≤ 60° O-9≤ y ≤ 1 O-4≤ y ≤9 O-1 ≤…

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Q: dx secx + 1 Transforming - -z² A 1+z² B z²+z 1-z² 1+z² Ⓒ 1- D √ -dz -dz -dz - 2z² 1+z² -dz using…

A: Here, the given integral is: I=∫dxsec…

Q: Let f(x)=6x²-5 to find the following value. f(t+1) f(t+1) = 0

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Q: x + 2 Determine the case of the following proper rational function after simplification: (x² - 4)(x³…

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Q: A 60m climbing rope was used in a tall building. How much work is performed in pulling the rope up…

A: Force function need to be constructed and then work done is calculated.

Q: If a horizontal element is used to find the area bounded by y=√√x, x=4 and the x-axis, the limits of…

A: We will have to find  qrea bounded by rhe curve  y= x1/2  X=4 and xaixs

Q: We can apply General Power Formula of Integration on which of the following integrals? I coshus / A…

A: In this question, we want to know that on which of the following integrals we can apply the general…

Q: Question 19 9 Let the integral be 'solvable' using trigonometric substitution. What is the correct…

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Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: If fx and gx are integrable on the closed interval a, b, and k is a constant, then to determine wich…

Q: In the indefinite Integral in(cosh x + ex)- A sinh x + ex In(cosh x + sinh x tex cosh x + ex In(cosh…

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