Find the limit. lim → 2 (1 i=4j+ 1² k) i. lim 1-2(ti-4 j+¹² k) = + j+ k

Q: mposition =

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Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 11x)y², y(0) - -…

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Q: Given: (1 + 2x) e-x dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the…

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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…

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Q: [x-²sec (an ² (2) dx 7 2tan ²2 (²) - 7tan² ( 1 ) - ₁ X + C 77 11 2ten* (²) 2³(-).c 2tan X - + +C 11…

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Q: b. The region R enclosed by the curves y = x and y = x² is rotated about the x-axis. Find the volume…

A: Given that region is bounded by the curve y=x and y=x2first find the intersetion point of the curves…

Q: II. Find dz Do not simplify your answers. 1. log,(√2x² + y) + tan(x − ³) = sin¹(x² - 1) +

A: We can solve this as follows:

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the value…

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Q: Question 16 A line through (-1, -2) with a slope of -10 has a y-intercept at

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Q: y"+9y=2e³x

A: Given; y''+9y=2e3x So, we can also write as; D2+9y=2e3x So, the auxiliary equation is; m2+9=0

Q: Find the partial derivatives of f(x, y) = x³y²

A: Solution ) f(x ,y ) = x3 y2 a) Partial differentiation with respect to x  fx( x ,y ) = 3x2y2 [ y is…

Q: Find F'(x). SOLUTION IN HANDWRITTEN x 1. F(x) = sin √t dt 2. F(x) = sin t² dt

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Q: Question 4 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of ax²+bx+c²…

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Q: what is the normal equation to the curve which is the circle with center at origin and and radius of…

A: Given circle , With center at origin (0,0) And a point on circle is (4,3)

Q: Describe the long run behavior of f(p) = (p+ 2)(p+ 4) (p + 5): As p →→ ∞, f(p) → ? ✓ As poo, f(p) →…

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Q: Find T(t) and N(t) at the given point. x = T(0) N(0) = = = e cost, yet sint, z = e; t = 0

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Q: Explain why you think the sequence 1-(-1)" con converges to a finite number or n+1 diverges. If the…

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Q: Let w = x³y cos(5z). Find the following. (a) g(x, y, z) = дw (b) Əy(x, y, z) = ду (c) o (x, y, z)…

A: Given data÷

Q: u be a differentiable function of du (a) (er) dr d du (b) = (6") = b. Inb dr dr 1 du (c) (In u) dx u…

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Q: x+1 1-x In [cosh (x+1) + sinh (x+1) lim 2tanh x=1- lim_ In x=1+ l

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Q: x²+x+1 Sa 2x²+2+3+x A B cb dx g(x) - dx = [Aƒ (x) − B ln(g(x)] + D fb da, and if A = ‚B <0, then dx…

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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: 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: Question 9 y Determine the domain of the function f(y) = (5y-4)²-81 Domain - [yy + } Write your…

A: For domain, we will check for what values function is not defined.

Q: Question 7 Given : A B E 0 2π 3 F|+ π 4 (U) =|m x³sin(2x) dx = 3 5π 6 3πt 4 277²-24 64 Find bif sbst

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Q: A courier service will deliver a package only if the length plus girth does not exceed 108 inches.…

A: Use the application of derivative and find the maximum volume.

Q: 1. Identify the equations of all the linear asymptotes of f.

A: There are three different types of asymptotes for a function fx: (i) Horizontal asymptote: If we…

Q: Let f be the function given by f(x) = (In x)(sin x). The figure above shows the graph of ffor 0 < x…

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Q: value(s) of x where the tangent line is horizontal for the function f(x) = x²(x – 5)³. tiple answers…

A: Topic:- application of derivatives

Q: The equation z² + 71-3-0 has two solutions A and B where A <B and A and B Give your answers to 3…

A: The given equation,          x2+7x-3=0

Q: Question 10 > Put a dot on the vertex of the parabola below. What is the coordinates of the vertex?…

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Q: c. The region R enclosed by the curves y = x and y = x² is rotated about the line y = 2. Find the…

A: Using disc method, volume of solid is evaluated.

Q: The IBP formula fudv=uv-fvdu Which of the following statements fits and satisfies the equations?…

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Q: Find the curvature K of the curve, where s is the arc length parameter. M(²) = (₁ + √2/2 =) ₁ - (₁ -…

A: we have to find curvature.

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the value…

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Q: Find the most general form of the antiderivative, F(x), of the function f(x) = −3√x - √√x. Provide…

A: Given fx=-3x5-x3 To find antiderivative (Integration)

Q: Definite Integral and Plane Areas of integration (snow solution) 3 1. dx Sö = 2 1+x 4 dx 2. Sh 25-x2…

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Q: Given the price-supply function p = S(x) = 10(e0.02x - 1), find the average price (in dollars) over…

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

A: Given  function f(x)=1x2+1 we want find the equation of tangent at the point where  x=1

Q: X A b B a C) C D d is solved by trigonometric substitution, which of the following (b) x = √5 sec8…

A: We can solve as follows

Q: Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. O elliptic…

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Q: Find the horizontal asymptote of f(x) = y = 5x + 2x³ +3 5x³x2-4

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Q: Question 8 3 (2x+4)³-8 } is

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

A: To evaluate: limx→3x-3tan9-x2sin22x-6 Given limit is of the indeterminate form 00 at x→3

Q: Write 20 terms of the Fibonacci sequence

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Q: Find the inverse function of f(z)-1+.

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Q: Consider using the method of partial fractions to solve x²+x+1 Sa 2x²+2+x²+x A In(x²+1) B x+2 D…

A: This is a problem related to integration of the function using partial fraction decomposition. Based…

Q: 1 xVx+3 xp:

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

A: limx→0 sin xx =1   and   limx→0 tanxx=1.

Q: Solve the following differential equations of -x 2y" - 2y + y = 2e¯*

A: If the roots of the auxiliary equation are complex α±iβ , then the complementary function is…