8. Evaluate each definite integral using the Fundamental Theorem of Calculus, Part 2. Ľ³ (1+2)(1-3)dt

Q: Solve the following initial-value problems starting from yo 6. dy dt A. - 7y y = At what time does y…

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Q: The function f(x) = 3 + 7x + 63x- -1 This function has a local maximum at x = with value and a local…

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Q: Find parametric equations for the line. (Use the parameter t.) the line through the points (14, 3,…

A: Topic- Equation of line through given points

Q: x²–2x (x+1)²* 3. Given the function f: x - a) Find the intervals on which f is increasing. b) Find…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: The objective of the question is determine the second solution of the given differential equation.

Q: Determine whether the work done along the path C is positive, negative. or zero. zero Ⓒ positive O…

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Q: simplify the function before differentiating f(x)= 1/square root e exponent 9x

A: Topic = Differentiate

Q: If u = x-y and v=x+y, then find the Jacobian matrix. о о о 312112342

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Q: S= 1 dx xinx

A: This is a problem related to integration. Please follow the procedure given below.

Q: 1. √x+2 dx X+1

A: Hi learner, we can answer the very first question as per the honor policy. Please resubmit other…

Q: Using the following graph of the function f, evaluate the limits (a) through (i). 10 8 Ay 2- of X 10…

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Q: 2. Let f(x) = 2x²-3x+1 ,x 0.5 Determine constants A and B such that is continuous for all values of…

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Q: Given the demand function D(p) = √300-2p. Find the Elasticity of Demand at a price of $14 0 X

A: We can find elasticity of demand.

Q: Find the constants a and b such that the function is continuous on the entire real line. 7₁ ax+b,…

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Q: Given the equation below, find dy dx = Y dy dx - 17x² + 7x68y + y ¹⁰ = - 9 dy Now, use to find the…

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Q: Find the number(s) b such that the average value of on the interval [0, b] is equal to 6. f(x) = 6x²…

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Q: The marginal cost for printing a paperback book at a small publishing company is c(p) = $0.016 per…

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Q: Express the equation in logarithmic form: (a) 45 = 1024 is equivalent to log4 A = B. A = and B = (b)…

A: This question is related to logarithmic equations, we will solve it using given information.

Q: 3 volume? A cylinder is inscribed in a right circular cone of height 3 and radius (at the base)…

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Q: A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it…

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Q: [In(cosw)tanwdw

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Q: [xcsc (y/x) - y]dx + xdy = 0 TEST FOR HOMOGENEITY OF DEGREE N: Let: F(x,y) = M(x,y)DX + N(x,y)dy…

A: The given differential equation is; [xcsc (y/x) - y]dx + xdy = 0

Q: Evaluate the following limit using Taylor series. 3 22²/2 (-) lim 2x² 848

A: Evaluate the following limit using Taylor series.     limx→∞2x2e-3x2-1

Q: Find the derivative. [미 In dx x +3 x-3

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Q: True or False? Let R be a ring and a, be R. Then a^2 - b^2 = (a-b (a+b) v a,b € R

A: We can check that the given statement is true or false.

Q: Identify the inflection points and local maxima and minima of the function graphed to the right.…

A: Topic- application of derivatives

Q: Graph the function. What symmetries, if any, does the graph have? Specify the open intervals over…

A: Topic = Function

Q: 3. Explain why lim √2x - 6 does not exist.

A: 3. The given limit is limx→32x-6 Note:    Multiple questions are given, we are answer with only one…

Q: Question Find the average value of f(x) = 5 cot (x) csc (x) - 2 over the interval [] Submit an exact…

A: As we know that; The expression for the average value of the function over the interval a,b is:…

Q: . (x + 2y) dx + (2x + y) dy = 0. ANS. x² + 4xy + y² = c.

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Q: and f(a) f(x) = 4x² + 5x² + 6x-7 3 7 2. Find f(x), f"(0), given

A: Given a function f(x)=4x3+5x2+6x-7 We have to the following of the given function, f''(x) f''(0)…

Q: 2.j -dx 2x2 x-1

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Q: FT [f'lt) = jwF(W) F(w) = jw f(w) => JA -T T tax + √(-_^) -jut e (-A) ²-just, AT Sim ² (WI) WT T A […

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Q: √ √x dx W|N 3 x2 + N/W N/W + C + C 2/3 + C

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Q: if 900 square centimeters of material is available to make a box with a square base and an open top,…

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Q: When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.03 cm /…

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Q: log₁ (3)

A: The given logarithm log449

Q: Write the equation in exponential form. Assume that all constants are positive and not equal to 1.…

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Q: Find x² - y²¹ lim (x,y) →(a,a) x² - y² O 2a O 2a² a² 00 DO

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Q: x dy-y dx = x3 dx y" Answer: 4x + x4y + x¹y = Cy.

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Q: the answer

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Q: Can you write out the solution in a better format please

A: Integral of (cot(x)csc(x) = - csc(x)   Csc(π/2) = 1 Csc(π/3) =2/√3

Q: You deposited $50 into a bank that offers 2.5% interest for 30 years. A: What is simple interest…

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Q: Consider the following differential equation: y" + y = sinx - 2e and the following boundary…

A: The given differential equation is y''+y=sin x-2ex

Q: Find the second derivative of y= b. -x-32 a. -3/2 4/24 C. -5/2 C. thrown vertically upward. The

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Q: Example 1 Find dy/dx, if a. y=sin(x² + 3x + 1) b. y = cos² (2x-1)

A: I have stated the used formulas in the solution

Q: Iƒ F(t) =î+tj+t²k and G(t) = tî+e¹+3k, then find (F × G)(t) at t = 0. 0 Ok O î+ ĵ + k o î+î

A: Topic- Cross Product of vectors

Q: ate the following integral using integration by parts. 4x sin x cos x dx u=4x sin x. Use the…

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 16x2 +…

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Q: 14. Evaluate f at its critical point(s). 15. Evaluate f at the endpoints of the given interval. 16.…

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