Find parametric equations of the line that satisfies the stated conditions. The line through (9, –5) that is parallel to 3 i-9j. O x = 9+3t, y = -5–9t O x = 3+9t, y = -9–5t Ox = 9+9t, y = -5-5t O x = 9–5t, y = 3–9t O x = 3+3t, y = -9–9t

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: ctor Calculus ints possible (ungraded) AS 2) Find the directional derivative of f(a, y, z) = x² + y…

A: Answer and explanation is given below...

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A:

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A: We need to find polar equation.

Q: Given the integral of S cos² x dx,

A: O integrate the given function.

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A:

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A:

Q: V. Let f(x) be a differentiable function such that for all æ > 1, • f(x) > 1, • f'(x) < f(x) and lim…

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Q: Question Approximate the local minimum value of the function given below. Use Newton's method with…

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Q: Find the sum of the convergent series. +0 | 3n+1 6n-1 n=0

A:

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A: Here we have to find the integration.

Q: Consider the tollowing Maclaurin series: (-1)"x2n (2n)! COS X = for all x e R. n=0 1. Let f(x) =…

A:

Q: an = In(n+1) – In(n) for n E N determine if the following is convergent or diverge An

A: limn→∞an=limn→∞ ln(n+1)-ln(n)=limn→∞ lnn+1n=limn→∞ lnn(1+1n)n

Q: (b) h(x) = v2x³ + 1

A: Topic = Derivative Only Question B is asked by student.

Q: **....... A rectangular parking lot with a perimeter of 440 feet is to have an area of at least 7000…

A: we have to find length range for the given rectangle.

Q: 2. Use integration by parts to evaluate the following. (a) Sx tan- x dx

A: LetI=∫xtan-1xdxApply integration by…

Q: an = In(n+1) – In(n) for n E N determine if the following is convergent or divergent { an } n=1

A:

Q: Test for exactness and find the general solution of: (cos2y – 3x²y²)dx + (cos2y – 2xsin2y – 2x³y)dy…

A: To solve the following differential equation

Q: Determine whether it is True or False does not converge (a) If an 20 for all n eN, then…

A: Comparison test: Let ∑n=1∞an  and ∑n=1∞bn be two series such that an≤bn ∀n∈N If ∑n=1∞an divergent…

Q: For the sequence defined by: a1 = 3 1 - 3 An аn +1 Find: a2 аз = II II

A:

Q: Find a polar equation for the curve represented by the given Cartesian equation. 9. a? + y? = 25

A: Given equation x2 + y2 = 25 To be found : Polar form.of given equation.

Q: Determine whether the following series is convergent or divergent (-1)"3n² 4n2 –1 (b) n=1

A:

Q: JVVy+1-2 dy can be evaluated conveniently if we let x =VVy+1 - 2 and dy = 4x(x² +2)dx. (A True B)…

A:

Q: 2 3 4 5 1'2' 4'8'

A: topic - formula for sequence

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A:

Q: 1.5 (3-x QI) Evaluate the integral dy dx using polar coordinate

A: Solving

Q: LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 1. (9Dª + 6D³ + D²)y = 0 2. (4Dª – 45D² – 70D – 24)y = 0

A:

Q: Evaluate the following iterated integral. 2 16 15y dx dy 2.

A:

Q: Find the particular solution of: ydx – 4dy = x²dy when x = 4 and y = 1 |

A:

Q: SV25-x² In dx , if we let u=/25 - x2 , then udu= - xdx. (A) True B False

A:

Q: Let an = n>1. In(2" +1) 1. Determine if the sequence {a,} is convergent or divergent. 2. Determine…

A:

Q: Find the volume of the given solid over the indicated region of integration. f(x.y)%3D4X+5y+7;…

A:

Q: Consider a continuous function f(x). The function has critical points at x = -7, x = -2, and x = 7.…

A: f(x) has critical points at x=-7 , -2 , 7Since f''(-7), f''(-2) is positive ⇒There is local minimum…

Q: 4. Find the Laplace transforms of the functions: (a) f(t) = t² (b) f(t) = t – 2e3t

A: a) f(t)=t2b) f(t)=t-2e3t

Q: determine if the series diverges or converges

A: This question can be solved using the concept of convergence and divergence.

Q: Evaluate the following double integral over the region R. 7 x-y') dA; R= {(x,y): 0<xS1, -1sys1}…

A: Here we have to evaluate the given double integral over the region R .

Q: > (atan (2n – 1) – atan (2n +3)) n=0

A:

Q: Problem 1 (а, Find the first partial derivatives of the function f(x, y) = x²yVy + 4y2. (b) fxyx of…

A: fxx,y = ∂f∂x  ;  fy(x,y) = ∂f∂y. fxyx(x,y) = ∂∂x∂∂y∂f∂x

Q: Determine whether the following series converges or diverges If the series converges, determine the…

A: The given series is:…

Q: Q2) Solve the D.E xdy + (2y – x* + 3x)dx = 0 %3D

A:

Q: x² - 25 The antiderivative of - dx is x2 -25 - sec-lx+ C. A True (B False

A:

Q: 18. Find the shaded area in the following figure. Assume that there are infinitely many squares and…

A: Area of Infinite shaded region Let Sk be the sum of area of each shaded regionthen…

Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

Q: ...................... Consider the following. 4 f(x) = (a) State the domain of the function, all…

A:

Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

A:

Q: Q3) Evaluate triple integral N S dz dx dy. x-y

A:

Q: Determine C, and C, so that y(x) = C¸ e²* + C2e* + 2sinx will satisfy the conditions y(0) = and…

A: Put x=0 in y(x).

Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

A:

Q: an = In(n+1) – In(n) for n EN determine if the following is convergent or divergent { an } n=1

A:

Q: E. Consider two functions f and g on [0, 7] such that I f(x) dr = 9, g(x) dr = 6, (2) dr = = 4, |…

A: