Question 1. Find y as a function of z if r*y" – 13ry/ + 49y = r°; y(1) = -10, 4(1) = -1

Q: Find the line tangent to the curve x + y3 = 4 at the point (3/3, –1).

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Q: Find the indicated value of the function f(x.y.z) = 3x - 5y? + 9z° - 6. f(9, – 3,1) f(9, - 3,1) = O

A: f(x,y,z)=3x-5y2+9z3-6f(9,-3,1)=3×9-5×((-3)2)+9(13)-6f(9,-3,1)=27-45+9-6f(9,-3,1)=36-51f(9,-3,1)=-15

Q: Q1. (а) Sketch the graphs and find the domain and range of the following functions: Coi () у 3D Vx —…

A: Range and domain of given graph is given : y= sqrt(x-5)  y = 1/(x-2)

Q: Q2: Determine which of the following functions u are harmonic. (a) 3x?y + 2x2 - y3 - 2y? (b) 2xy +…

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Q: -1 (3). Let g(x, y) = e2y tan value of g does not change. - 2. Find a direction from the point (1,…

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Q: 6. If f(x) = x2 + 2x - 1 and g(x) = 2x-3, find each of the following functions. (a) f°g (b) g°f (c)…

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Q: Eliminate the parameter in the curve defined below to write y as a function of x 1 x = 1+zt and y =…

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Q: 9. Find f°(x) given f(x) = 7(3x – 4)* + 5ex

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Q: 1. Find the intercepts of the function. f(x)-x* +2 а.

A: Given data÷

Q: 4.2 Calculate the length of the tangent AB drawn from the point A(6; 4) to the circle with equation…

A: Step 1: The triangle formed by the point - center of the circle O, point A and point B would be…

Q: Find y as a function of a if y(1) = −2, y′(1) : = 4. y = x²y" + 9xy' + 16y = = x³,

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Q: . 4. Find y as a function of x if x?y" – 7æy + 16y = 0, 2. || y(1) = -5, y'(1) = -4.

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Q: y = sin(2x – 27)+1

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Q: c) Find 4°f(x) if f(x) = (3x + 1)(3x + 4)(3x + 7).. (3x + 19).

A: GIVEN: f(x) = (3x + 1) (3x + 4) (3x + 7).... (3x + 19)

Q: A particle moves along the x-axis so that its velocity at any given time is = 2t - 3 and x (0) = 3.…

A: Introduction: The extrema of a function are the maxima and minima. The highest and minimum values of…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.