7) FIND EQUATION Of THE TANGENT AN LINE TO THE PARAMZTRIL X=t-+もt こe AT t =0. CURVE

Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

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Q: 4 1 T/2 Зл/2 -1 -2 -3 -4 -5 The graph of the function f(x) = cot x is given above for the interval a…

A: From the graph of f(x)=cot x, we have to find its asymptotes

Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

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Q: Determine the generating function of the following sequence {0, 0, 0, 1, 1, 1, ....}

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Q: Find the first four nonzero terms in the Maclaurin series for f(x). f(x) = e 5x sin x ... Choose the…

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Q: d²y Given that x +y³ = 2, prove that dx2 4.

A: Given: x3+y3=2   As we know that; The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2

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Q: Activity 1.5.2. A potato is placed in an oven, and the potato's temperature F (in de- grees…

A: Solution: Given data

Q: Determine whether the improper integral diverges or converges. -6x dx O converges O diverges…

A: This is a problem related to indefinite integral. Based on the general formula and concept we will…

Q: Now, let's discuss the difference cases of solution to a given system of linear equations. There are…

A: Given problem :- Now, let's discuss the difference cases of solution to a given system of linear…

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Q: Solve the following integrals: 1. S 7e*dx 4. S 12*+1dx 5. S-dx 2. S(5ex – 6*)dx 3. Ј 3(5)dx 6.…

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Q: d²y of the following equation then simplify whenever possible. 3) Find and dx dx- x = 3em y = 4e-m

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Q: Find the arc length L of the graph of r(t). r(t) = 5 cos(t)i + 5 sin(t)j + tk, 0<t< 2n L =

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Q: principle of mathematical induction

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Q: A tank is being filled with a liquid. Z (1), given below, is the amount of liquid in liters in the…

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: arc on y = x12 from (0, 0) to (4, 8) 528/5

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Q: | (2x - y) dx + (x + 3y) dy. Evaluate C: arc on y = x5/2 from (0, 0) to (4, 32)

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Q: 1. What is the derivative of f(x) = x2 – 8x + 12 when you illustrate using tangent? 2. What is the…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: Given the function g(x) = 8x³ + 12x² – 48x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

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Q: Use the graph of the function f(x) shown below to evaluate lim f(x). x 3+ 3 2 3 O 3 O 1 O DNE 2.

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Q: integrate (2x + sqrt(x)) dx from 3 to - 6 A. 27 +2√3+4√6 B. 27 + 2√3 C. 27 - 2√3+ 4√6 D. 27-4√6

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Q: Determine whether the improper integral diverges or converges. 0. 8x xe dx -o. converges O diverges…

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Q: 5 4 3 1 T1/2 3π/2 -1 -2 -3 + -4 -5 The graph of the function f(x) = cot x is given above for the…

A: Solution is given below:

Q: Evaluate the improper iterated integral. 9. x2 dy dx 1 + y?

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Q: Зх -5 dx (x+1) (x+2)²

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Q: x2 - 6x + 8 lim X 2 X - 2 1

A: The objective of the question is evaluate the limit.

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Q: Consider the following equations. f(y) %3D У(5 — у) g(y) = -y

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Q: Find the derivative of the following equation x+3 x-4 (a-4)° 2x (x-4)² 7 (x-4) 2x-1 (x–4)°

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. 8j i2 + 3

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Q: Find the value of the derivative of g (x, y) when we restrict to the curve defined by x = cos t and…

A: Differrtiate with respect to t

Q: What is the third derivative of the function: f(x) = x5 - 4x³ + 3x?? O 5x – 12x² + 6x O 20x? 24x + 6…

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Q: _4. What is the first derivative of f(x) = (x² – 4)(3x – 2)? а. 9х? - 4х — 12 b. (2х)(3) C. 6x d. (x…

A: Topic:- derivatives

Q: Determine whether the series E. (-2)" is convergent or divergent. If it's n=1 convergent, find its…

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Q: Find div F and curl F if F(x, y, z) = 3y°z©i – 3x*z°j – 3xy*k. div F= curl F=

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Q: Find the limit. NOTE: Enter the answer using round brackets. t? + 7 lim t 612 + 7't 1° = (?, ?)

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Q: Describe the graph of the equation. r = 3cos ti - 4 sin tj +k O An ellipse in the plane x = 1,…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: 2 2. Find an equation of the plane containing the point P(0, -) and the line determined by the two…

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Q: Verify Green's Theorem by evaluating both integrals ÔN I y? dx + x2 dy = dA ay ax 'R for the given…

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Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 7…

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Q: Find the first partial derivatives with respect to x,y and z. f(x. y.z) - 3x°y - 9 xyz + 10 yz %3D

A: Find first partial derivative

Q: 1 T/2 3t/2 -1 - -2 + -3 + -4 - -5 The graph of the function f(x) = sec x is given above for the…

A: Topic:- function and calculus

Q: Evaluate the definite integral. Using Fundamental Theorems Calculus. sin x 4 – x² dx V1 + x2

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Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

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Q: ||r'(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = t²i + t°j %3D K(t) =

A: Given: r(t) = t2i +t5j Solution: r'(t) =ddtt2i+t5j =2t i +5t4j r"(t) =ddt2t i +5t4j= 2i + 20t3j

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

A: This is a problem related to vector calculus. Based on green's theorem we will solve the integral.