For the Limits of Logarithmic Function, we should consider that limx→a ln g(x) = ln g(a) where g(a) should be

Q: - courses / MATH1200 / Current Activity / Worksheet 1 From the following results, determine whether ...

A: Topic:- application of derivatives and calculus

Q: dy Find using implicit differentiation, for the equation x° + y° = 10 is da %3D y7 y5 y5 o O O O

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Q: Find the exact arc length of the curve over the stated interval. y = 3x/2 - 2, from x = 0 to x = 1 %...

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Q: rotated about the x- axis

A: Solution is here 

Q: Given the matrix and its eigenvalues 3- 1-R 1 becomes has eigenvalues R = 1 + i -1 1-R Find the new ...

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Q: d Compute [(2r* + 5)(4x–1] at x=} 2 24 Your answer

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Q: logarithms to find an exact solution for   ln(5)+ln(5x2−3)=ln(154).   If there is no solution, e...

A: Given query is to find the value of x.

Q: Evaluate: ,(3y6 – 8y* + 9y?)dy

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Q: Find the area of the region bounded by y = -x² – 4x – 2 and y = 2x2 + 8x + 7.

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Q: Sketch the region enclosed by y = 4x and y 4x2. Find the area of the region. %3D

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Q: 2x + 4, a<4 om the following results, determine whether the function f(a) = { 8, a = 4 -x + 16 a 4 i...

A: Given query is to find function is continuous or not at x = 4.

Q: Find the volume of the solid generated bounded by x = Jy – 1, x = y? – 2y + 1, rotated about the x- ...

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Q: Use any method to determine whether the series converges or diverges. 00 1 Σ 2 + 7-k k=1 O The serie...

A: Given query is to find series converges or diverges.

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: Find the area bounded by the parabolas (x 1) 4ay and y2 + 4a = 4ax.

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Q: a) Determine the cosine of the angles of the triangle whose vertices are A(1, –-2, 1), B(3, 0, 2), C...

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: (a) Given: - The condition is the same direction as -2i+9j. To find: - The unit vectors that satisfy...

Q: Given the vector function *(t) = (t, cos (2t)) Calculate the curvature when t=5.4

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Q: ,5x-2 If f(x) = 2 + e%r-2 %3D then f-'(3) = %3D

A: Topic = Functions

Q: If f(a) = 7cot- * +2, then find the value of f(-4) is, 17

A: Given query is to find the derivative and indicated value of x.

Q: Let u, v and w be vectors in Cn . Clearly prove that (u + v) · w = u · w + v · w.

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Q: 4 ry sin (x? + y*)dxdy Find

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Q: 8. arctan (-1)

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Q: The graph shown below is fx) = -(x - 1)2 + 5. What is the integral function g(x) that defines the ar...

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Q: TT S sin () Evaluate: 8 cos? dx

A: We will find the value of the integral. 

Q: dy Find using implicit differentiation, for the equation x + y³ = 9 is. dx

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Q: *xsin-'xdx The antiderivative of is x-V1-x2 sin-!x+C A True (B) False

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Q: (주) X X Evaluate: " sin' cos* () d 4

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Q: lim In (xth)-Incn) X-DO

A: Topic = Limits

Q: 4 Find the value of f'(-1) if ƒ (x) =. (3xr² – 2x +1)

A: we have : f(x) = 4(3x2-2x+1)3 To find :f'(-1)

Q: - 1] Q2 a. Find the eigenvectors of the matrix b. Solve the ordinary differential equation: dy Y-e d...

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Q: 3x-4x+1 if x + 1 if x = 1 3. Given the graph of the function f(x) = complete the table. X-1 Differen...

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Q: Suppose f " is continuous on (-o, o). (a) If f '(-3) = 0 and f "(-3) = -9, what can you say about f ...

A: Given that, (a). f'(-3) = 0  and   f''(-3) = -9 (b). f'(5) = 0  and   f''(5) = 0 We have to choose c...

Q: Evaluate the following limits for h(x) 6x + 1, I 6 and Justify your answer. (0 lim h(r) (i) lin h(t...

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Q: g(x) = 190 + 8x3 + x4 (a) Find the interval of increase. (Enter your answer in interval notation.) F...

A: Given g(x)=190+8x^3+x^4

Q: find eigen value of matrix A 3 -2 A %3D -니 2. 2.

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: In|1+49| + C = of the given choices In|l+49 + C

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Q: DÒ NOT include spaces in between characters. * Given F(x)= f(x)g(x) and f(2) = -3, f'(2) = 4, g(2) =...

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Q: Determine whether the series converges. k=1 The series

A: The given series,       ∑k=1∞k4e-k5

Q: Provide an equation of one of the common functions with multiple transformations. For example, f(x) ...

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Q: The integral of tln i with respect to t is; © none of the given choices Oin-3)+c ln-1)+C

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Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per second...

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Q: az az Find and e = 5x 2² + sin(r + 2) – y?.

A: Find the partial derivative of z with respect to x and with respect to y respectively

Q: 2 cos 20 sin? 0 + 2 cos 0 cos 20 sin 0 + cos 20 cos? 0 d0 (use trigonometric integrals)

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Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t? from t = ...

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Q: Maximum Volume A package to be sent by a postal service can have a maximum combined length and girth...

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Q: Solve the problem. Round your answer, if appropriate. A man 6 ft tall walks at a rate of 3 ft/sec aw...

A: We can find the required answer as below.

Q: Find the total area between y = x'/3. - x and the x - axis for -1 sIs8.

A: Follow next step

Q: Prove Jhab sinY Tim lim e-1 lim Sin y ニ ン と Siny S iny

A: Given,            limx→0sinxex-1=limx→0ex-1sinx=limx→0esinx-1xTo find : Prove the given limits.