4. Determine the vertical asymptote(s). x'+5x-7 а. У - х*-3х- 28 x³+4x³ -4x+6 b. f(x) - * x'+2x² -5x-6

Q: Find the oblique asymptote of 2z2-9z+15 f (x)= I-5 Section 3.4 O y = 2x + 1 y = 2x-19 O y = 2x- 9 O…

A:

Q: find the horizontal asymptote(s) for…

A: Simplify the numerator and denominator of the function as follows.

Q: 3. Determine the slope of the tangent at x = -1 on the graph f(x) = (5x² + 1)3.

A:

Q: Find the equation of the tangent line to the graph f(x) = 2x² + 5 at P(-1,7)

A: We will find out the required equation of tangent.

Q: The graph of f(x) = 5(x – 1)2 – 6 is a parabola that opens --Select--- , with its vertex at (x, y) =…

A: Given equation  f(x) =5x-12-6

Q: The graph of f(z) = 2z³ + 12z² – 126z + 17 has two horizontal tangents. One occurs at a negative…

A: for the horizontal line find the slope first and set to zero.

Q: The slope of the tangent line to the graph of the function y = 2x3 at the point (2, 16) is lim2"…

A:

Q: 5. Hance sits at one of the points on the curve y = 2x³ -3x²-12x +20 where the tangent is parallel…

A: Please see the below picture for detailed solution.

Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: Find the minimum and maximum of the function y = z° – 6480z on [-7,7] by comparing values at the…

A: The function is y=z5-6480z and the given interval is -7,7. To find the critical points of the…

Q: G&)= In (5x t10) + 1, 1 State and domain, vertical asymptote end behavior. As approches vertical, Gx…

A: Let G(x)=ln(5x+10)+1.1 The domain of the function is the set all x-values on which the function is…

Q: Find the shortest distance from x²+3y²=12 to the point (4,2).

A: We have to find the shortest distance from x²+3y²=12 to the point (4,2).…

Q: Find the orthogonal trajectories for the family of curves 3x2 − y2 = C. Use a graphing utility to…

A: Given:  The family of curves: 3x2 − y2 = C

Q: The slope of the tangent line to the curve at (x,y) point is defined by 3log3 (1- ) (k +1). If the…

A:

Q: 9). Find the curve whose slope at any point is 3x – 5 that passes through point (5,3).

A:

Q: Find an equation of the line tangent to the graph of ƒ(x) = (2x - 1) (x + 4) at (1, 5).

A: To findEquation of the line tangent to the graph y=(2x-1)(x+4)  at (1,5)⇒y=2x2+7x-4.

Q: 2. Find the equation of the horizontal asympto

A:

Q: O Fend an equalion of the tangont line to the graph-of y-x-4Vx at (1-3). O Find an equalion -of #he…

A: If the slope of a line and any point (x1,y1) on it is known then its equation is given by :…

Q: How can we find the horizontal and vertical asymptotes of the curve?

A: We find the horizontal and vertical asymptotes of the curve

Q: 9) Write an equation of the tangent line to the graph of y = 5x2 - 8 at the point where x 0. %3D -3x…

A: Quotient rule of derivative of the function f(x)=u(x)/v(x) is

Q: Find the equation of the line tangent to the graph of f(x) = 4x° + 6x2 – 6x – 5 at x = -6. %3D

A: The function is given by fx = 4x3+6x2-6x-5 To evaluate: The equation of the tangent line to the…

Q: At which x location on the graph of f(x) = -x² - 2x + 15 is the slope of the tangent 0?

A:

Q: 2-→ Find-the-residues-of-the-function-at-its-poles F1:(z) = (2-z-+3):/(z²-4)¶

A: We need to find the residues of the function F1(z)=(2x+3)/(z2-4) at its poles.

Q: 4. What is the area of the largest rectangle that can be insribed in the first quadrant under the…

A:

Q: Q#4: (i) What is the projected level of revenue in 3 years for a company with current revenues of…

A: (i).       The present value is the value of the sum received at time 0 or the current period.  It…

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: Find the equation of the langents to the graph y-x3 3x2-15x-20 at the points of the graph where the…

A:

Q: 4. Find the slope of the line tangent to the graph of 1 f (x) = 2x4 – 32x3 + 17x2 – 9x + 4 at x 2 -…

A:

Q: N(t) components per day after t days of traning where N(t)=75t/t+5 t> or = 0. Sketch the graph of N…

A:

Q: Sketch the graph of y = (x² – 1)² – (2x – 1)². [In your answer, you must include the following: •…

A:

Q: Given the preconditions for x and y as |x – y| ≤ 200, |2x + y - 150| ≤ 250, show the post-conditions…

A: Given that, z=3x2+y2+3xy-7x-8y+10 Subject to  x-y≤200 2x+y-150≤250

Q: The slope of the tangent line to the graph of the function y = 8Vx – 2 at (4, 14) is 2.00 3.50 -3.50…

A:

Q: Find the equation of horizontal asymptote of y=3(0.2^x)+15pi

A:

Q: 7. What is the equation of the asymptote for the function f(x) = 3(2x+³) + 2 a) y = -5 b) y = 3 c) y…

A:

Q: Find the horizontal and vertical asymptotes of the curve. 6x²+x- - 9 у x² + x - 56 X = (smaller…

A:

Q: 7. Find the slope of the tangent line to the graph at (1,1): x2y? - 9x2-4y2 = 0 x-9-4-0 (-4, 2/3)…

A: x2y2−9x2−4y2=0 Use implicit differentiation to find the slope of x2y2−9x2−4y2=0 Implicit…

Q: 1. Find the slope of the graph of the function f (x) = v3x + 4 at x = 7. Then find an equation of…

A: equation of tangent line is (y-y1) = slope (x-x1)

Q: Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and…

A:

Q: Compute the equation of the horizontal asymptote of the curve y = (2x- 1)/ (x + 2). y = 2 x = 2 X =…

A: Given; y=2x-1x+2   As we know that; To calculate the horizontal asymptote, solve the limit…

Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A:

Q: A company that produces ribbon has found that the marginal cost of producing x yards of fancy ribbon…

A: From the given information, the total cost can be determined as ∫01000C'xdx. That is,…

Q: Can you help with this problem step by step?

A: Given: -

Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: 4. Jacobi is seated on the line tangent to the graph of  y =2x3 -3x2 -12x +21 at x =2.

A:

Q: 8. Determine a quadratic function f(x) = ax² + bx + c if its graph passes through the point (2,22)…

A:

Q: graph of f(x) = 4(x – 2)² – 7 is a parabola that opens --Select- v with its vertex at (x, y) = ( and…

A:

Q: is the total cost of production for a 7-hour day, where x machines are used to produce jackets and y…

A: The Extreme value theorem states that if a function is continuous on a closed interval a, b, then…

Q: The demand for face masks is given by p =-3 In(x) + 10 with domain [1, 28] where x is the number of…

A: Given: The demand for face masks is given by, p=-3 lnx+10, with domain 1, 28 where x is the number…

Q: Determine the area of the triangle formed by the tangent to the graph of the function y=3-x2 drawn…

A: Given,            y = 3 - x2 , and the point 1, 2

Q: Sketch the graph of y = (x² – 2)² – x². [In your answer, you must include the following: • Find the…

A: We have to sketch the graph of function y=x2-22-x2

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.