Which of the following is an acceptable answer, when we are asked to evaluate f 5+x² O In sec+tan 0 + C In √x² +5 √5 ++ C + C sec √x²+5 √5 dx?

Q: Given: planes II₁ : 2x - 5y + z = −1 and II₂ : x + 5y + z = 5 intersecting on a line l (a) Compute…

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Q: Find the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1)…

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Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x - 2).

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Q: In this problem, you are asked to carefully read Example 6.4.2 of APEX Calculus. 1 The given…

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Q: dy Find by implicit differentiation, given that x²y – 2y6 = =-5. Your answer could involve both dx x…

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: The objective is to find the slope and equation of tangent line.

Q: Differentiate the function: y = e-x cos²x x²+x+1

A: To differentiate the function.

Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) x→1 x+3 a. Find lim f(x) or…

A: Here is the solution of the given problem. To, solve this problem we use the simple criteria of…

Q: ind g'(3) given that f(3) = -1 and f'(3) = 5. (a) g(x) = 2r³-7xf(x)

A: Topic:- application of derivatives

Q: In an autocatalytic chemical reaction, the product form is a catalyst for the reaction. If Qo is the…

A: SOLUTION-

Q: For which of the following integrals should substitution be used, instead of Integration by Parts?…

A: Solution :option D substituition be…

Q: A company determines that its total cost, in thousands of rands, for producing x  items is (image…

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Q: 3 [*² [b³ – y³]² dy

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Q: 1. A certain ellipse is centered at the origin from which the major axis is always equal to 25 and…

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Q: . Expand the binomial (2x - 1)*.

A: Binomial theorem

Q: The coordinates of the end of a line is at P (0, 0, 1) and at Q (1, 1, 1). Represent mathematically…

A: Given that the coordinates of the end of a line is at P (0, 0, 1) and at Q (1, 1, 1). So the…

Q: 2. Given: polar curves C₁ : r = √√√2- cos 0 and C₂ : r = √√√2 + sin intersecting at A(³√2, ³) and…

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Q: 7. Compute the Jacobian of the following transformation. x=u²+uv y=3uv².

A: The given data is: x=u2+uvy=3uv2 To find the Jacobian transformation.

Q: Use the left-endpoint approximation to approximate the area under the curve of f(x) = +1 on the…

A: This question can be solved using the concept of approximation of area under curve using left…

Q: Estimate the slope (slope rise/run) of the tangent line to the curve. N 3 4 6 N D-

A: topic- slope of a line

Q: ind the open intervals on which the function shown in the graph is increasing and decreasing.…

A: Topic:- function

Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x - 2).

A:

Q: N|- x² Given: quadric surface S with equation (y - 3)2 - 2 (a) Determine and identify the traces of…

A: Quadratic surface S with equation y-32-x22-z22=1

Q: y" (ex®-3x2+5)4 (Type an expression using x as the variable.) 증

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Q: (ii) tank (In x) = x²-1 x² +1

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Q: Determine the value of x when the slope is its maximum for the function f(x)=2cos(3x)

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Q: o - 23 dy

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Q: (B) Find equations of the tangent and the normal lines to the curve y-exy = sinh x² +ln(x+√y point…

A: Given the curve y-exy=sinhx2+lnx+y at the point P0,1

Q: (b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy +…

A: We have to find the general solution of the given differential equation using variation of…

Q: Find the equation of the tangent line to the graph of the function f (x) = sin (7√) at the point…

A: Here we have to find the equation of the tangent line of the function…

Q: 2. Consider the circle C₁ : r = 1 and the roses C₂: r= cos 20 and C3 : r = 2 cos 20, each of which…

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Q: lim f(z) = #t * NE

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Q: Please

A: We will solve the problem.

Q: Find an equation of the line tangent to the graph of f(x) = (4x-3)(x+2) at (1,3). The equation of…

A: topic- equation of tangent line to the graph

Q: f(x) = 2x³9x² + 12x − 3 -

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Q: Evaluate the following integrals. -1 L₁ (3²- (3x² - 4x−¹+2) dx

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Q: draw and identify the graph of the following surfaces a. z = √9-y²

A: Given

Q: Question 4 Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

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Q: A wind is blowing giving the projectile the acceleration of 9m/s2 in the positive direction of the…

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Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

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Q: Use f(x+0.0001)-f(C) 0.0001 f(x)=52²-7x ata = 2, to the nearest tenth. to determine the…

A: Given function f(x)=5x2-7x

Q: Question Find the area of the region that is bounded above by the curve f(x) = (x + 8)2 and the line…

A: This question can be solved using the concepts of area bounded by curves.

Q: Let f(x) = { 6 - x - x² if x ≤ 2 2x - 7 if x > 2 Calculate the following limits. Enter "DNE" if the…

A: On solving this we will get

Q: x² - 25 to fill in the table: Xx - 5 6 5.5 5.1 5.01 Based on ONLY the table of values above, what…

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Q: x-4 x²+2x-15 Inx+51-Inx-31+ C 8 Option 1 S: dx 1 (x + 5)⁹1 Je In + C + x-3 -100 1 9 In|x + 5|ln|x −…

A: We can find the answer as below

Q: a.) Solve the equation z³ − 1 = 0 15 1 √3 b.) Evaluate (-+-+3) " 2 2

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Q: 2. Determine parametric equations of the line that.... 4 a) passes through (-9,8) with slope - 5 b)…

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Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

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Q: a. Use the definition mtan = lim f(a+h)-f(a) h h→0 b. Determine an equation of the tangent line at…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: 6. Determine the Cartesian (scalar) equation of the plane that... a) contains the points (6,1,0) and…

A: SOLUTION-