Find the directional derivative of f(x, y) = direction of Q(2, —2). NOTE: Enter the exact answer. Duf = 5x x + y at P(5, 0) in the

Q: II. Find Do not simplify your answers. dr 1. log,(√2x² + y) + tan(x² − z³) = sin¯¹(x² − 1) + −

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Q: The Cayley-Hamilton Theorem states that a matrix satisfies its characteristic equation. For example,…

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Q: [w (1-32)] 3w 11. lim w In 1 In W→∞

A: LetL=limw→∞ wln1-23wFor L hospital L=limw→∞ ln1-23w1wNow apply L hospital ruleL=limw→∞…

Q: π/4 x³ dx (x²+4)5/2 ST/4 (Use trigonometric substitution)

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Q: √x²-9 √ di Using trigonometric substitution, what is f - dx ? x3

A:

Q: (D² — 4)y = 8e²x — 12 - -

A: Given; D2-4y=8e2x-12 So, the auxiliary equation is; m2-4=0

Q: 12. lim [ln(t) sin(t)] t→0+

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Q: Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 4 4. lim log(x+3)…

A: Given: limx→1-log12x+31-coshcos-1x

Q: . The voltage,V, in a circuit is slowly dropping at a rate of -0.01 volt/sec as the battery wears…

A: I have appended the formula used in the solution part.

Q: 1. xý + 3y += sin x v2

A: Given :

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 4x+14 between x =…

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Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: Let's find.

Q: Describe the graph of the equation. r=-13 i+(1-t2) j+t k O It is a parabola in the plane x = -13,…

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Q: Using trigonometric substitution to solve: f 1 A + C 8 sec x√4-sin2x sin 2x + C 4 cos x√4-sin²x sin…

A: Solution is given below:

Q: 1. Evaluate the following limits. Using L'Hôpital's Rule is not allowed 3. lim (x-3) tan(9-x²)…

A: We will calculate the limits by Limits rule

Q: x²+x+1 Sa 2x²+2+x³+x² (A (B (D) -b dx dx = [Aƒ (x) – B ln(g(x)]å + D ſb da , and if A = ‚B < 0, then…

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Q: A B C The IBP formula fudv=uv-fvdu can also be written as f udv + ſ vdu : = UV Which of the…

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Q: Determine whether the sequence a₁ = find the limit. Show All Your Work! 1+9n² 1+n² converges or…

A: To determine whether the given sequence converges or diverges.

Q: V. Given: if x ≤ 2 el3r-6-2, [2x - 5], 13 f(x) if 2 3 √x²9, 1. Determine if f is continuous or…

A: Solution is given below:

Q: Calculate[ri(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and then by…

A: This question can be solved using the concept of dot product and cross product of two vectors and…

Q: if any. Find the absolute extremum point (s) of f(x) = el-cosa on [-, ],

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Q: f/²sin (co COS () sin (²) dx (Consider initially the first 2 terms) ATT/A a dr

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Integrate the following functions f(x,y) = 3x-2y. R: over the given regions. the circle x² + y²

A: Given function f(x,y)=3x-2y and region R is x2+y2=1

Q: Evaluate the definite integral. NOTE: Enter the exact answer. S||ti + t²i||dt =

A: The given integral is converted to another form by using the following formula and then evaluate the…

Q: How many different 8-digit phone numbers do not contain the digit 6? Assume that any digit in the…

A: To determine how many different 8‐digit phone numbers do not contain the digit 6. Assume that any…

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

A:

Q: IV. Do as indicated. 1. Let f(x): = where x = 1. 1 Find the equation of the tangent line to the…

A: Given equation f(x)=11+x2Differentiate…

Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

A:

Q: Using trigonometric substitution, what is √x²-9dx ? f x3 A sec (-) √x²_9 6x² +C B ¹ (1) - V +C (ⒸC)…

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Q: II. Find d Do not simplify your answers. 1. log,(√2x² + y) + tan(z* — x") = sin−¹(x² − 1) + ½

A: This question can be solved using the concept of differentiation of implicit function.

Q: 1. ) cos (4) COS -π/2 f/² sin (1) sin (²) dx (Consider initially the first 2 terms)

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Q: Write an equation for a rational function with: Vertical asymptotes at x = 5 and x = -2 x-intercepts…

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Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

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Q: Given the function f(n) = 3n¹ +33n³ +90n²: its f-intercept is its n-intercepts are

A: We can find the intercepts as below in the following steps.

Q: Integration by Parts 4. fxe4x dx 5. [ e* cosx dx

A: This question can be solved using the concept of integration by parts.

Q: Identify the surface that corresponds to the equation 3y^2 - 2x - 8z^2 = 0. O elliptic hyperboloid…

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Q: dy II. Find Do not simplify your answers. dx 1. log; (√2x² + y) + tan(2* — 7³) = sin¯¹ (2²-1) + - Б

A:

Q: An integrating factor is μ(y) = The solution in implicit form is = c, for any constant c.

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Q: Find all Max., Min., Saddle point for the functions below: P(x) = 2xy-5x²-29² + 4x +49-4

A:

Q: V. Given: 2. Find f'(2), if it exists. el3z-61-2, f(x)=[2x - 5], √x²-9, if x ≤2 if 2 3

A: Solution is given below:

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 1+ 1. lim. 2-12x²+x-1

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Q: Identify the center of the conic section whose equation is 4x 2 - 25y 2 - 8x - 100y - 196 = 0. (-1,…

A: We can identify the center as below.

Q: Describe the end behavior (long run behavior) of f(x) = 28 As → →→ ∞, f(x)→ ? As I→ ∞, f(x) → ? v

A: This question can be solved using the concept of limits.

Q: 15x² x3-43x - 19 - (x + 1)²(x² - 6x +13) Ax + B S ax²+bx+c The integral What is the value of dx can…

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Concept: As we know that a equation of the line through the point (α,β,γ) and perpendicular to the…

Q: IV. Do as indicated. 1. Let f(x) = where = 1. 1 Find the equation of the tangent line to the graph…

A: Let's find.

Q: Use linear approximation or differentials (but not both) to estimate: cube root of 7.98 Is your…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the length s of the circular arc. (Assume r = 5 and ? = 130°.)

A: s =r*θ θ in radian s = 5*130π/180 s =11.34

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, 2A-3B…

A: