29. a.If f(t) = 1 −u1(t), find ℒ{f(t)}. Sketch the graph of y = f(t).

Q: 18. Find the denvative or the runction y = 2x - 13x + 5 and use it to find an equation of the line…

A:

Q: If the slope of the tangent line to the graph of y%3f(x) at x-Da is m(a)%=D2a+1, and f(1)=5, then…

A: Given: If the slope of the tangent line to the graph of y=fx at x=a is ma=2a+1and f1=5. To Find: f2…

Q: 7. Find the equation of the tangent line to the graph of the function 4xy + 5 In y = 28 at the point…

A:

Q: 16. Find the equation of the tangent line to the curve y = e* at the point (a, f(a)) when a = In 3.

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: 2. Find a point on the curve y = e 3x , at which the tangent line passes through the origin.

A: Solution: The objective is to find the point on the curve y=e3x at which the tangent line passes…

Q: Show that the slope dy/dx is defined at every point on the graph of 2y = x² + sin y.

A: Given- 2y=x2+sinx To prove- That the slope dydx is defined at every point on the graph of the above…

Q: Find the equation of the tangent line to the graph of f(x) = In x at xo = e 8.

A:

Q: What is the slope of the tangent line that touches the graph of In y + e2=-1 = 3y – 4x at the point…

A:

Q: 4. Determine the point(s) at which the graph of f (x) = has a horizontal tangent. Simplify as much…

A:

Q: What is the slope of the tangent line that touches the graph of In(y) +e-=3y– 4x at the point A В) з…

A: slope , m=dydx.

Q: 3. Find the equation of the tangent line to the graph of y at the point (1,0) given 2r² where r> 0.…

A: Given that: xy+1x2=2x2+y

Q: 4. At what point on the graph of y =x2 is the tangent line parallel to the line 2x – 4y = 3?

A:

Q: 1- find dy/dx as a function of x. y = sec (tan x) 2- find dy/dx etty = 2x + 2y %3D 3- find an…

A:

Q: he line tangent to the graph of y=In(3x)+ 2x e at x =1 6

A: Equation of line is given as   y-y0 = dydxat x=1*(x-x0) Given,x0 = 1y = ln(3x) + e2x6y0 = ln(3x0)…

Q: 1) Find an equation to the line tangent to y = (x – 3) 2 at x = 0.

A:

Q: 1 Find an equation of the tangent to the curve f(x) = /x + 8 that has slope 4 %3D - OA. 1 y =7x-3 O…

A: Equation of the line in slope-point form is:        m = slope (x1, y1) = point on the line

Q: 3) Find an equation of the tangent line to the graph of y = (z + 4)² at z = 4.

A:

Q: 6. The slope of the line normal to the graph of y = 2 In(sec x) at x is 4

A:

Q: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

Q: 6. The tangent to the function f(x) = ke2x at x = has slope 2e. Find the value of k.

A:

Q: 5. Find an equation of the tangent line to the graph of f(x) = In (2x + 1) – e* at the point where x…

A:

Q: Find the lengths of the curves y = x2 - (ln x)/8, 1≤ x ≤ 2

A:

Q: This is the equation of the line tangent to the graph of * y = x2 + 3 at x = –1

A:

Q: 8. Find the equation of the tangent line to the curve y = e* at the point (a, f (a)) when a = In 3.

A:

Q: What is the equation of the tangent line to graph of the function y = e^(3x) at the point (0,1)? O y…

A: The given function is y=e3x

Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

A:

Q: Does the graph of Sxsin(1/x), x + 0 g(x) 1o. x = 0 |have a tangent line at the origin? Give reasons…

A:

Q: Find an equation of the tangent line to the graph of y=e^-x^2 at the point (2,1/e^4)

A:

Q: -Find the equation of the tangent to the function y = sin x at x = t/4

A:

Q: 7. Determine the equation of the tangent to the function E-2 f(x)=- at x= 1.

A:

Q: Find an equation of the tangent line to the graph of y = e−x2 at the point 4, 1/e^16

A: Given curve

Q: 3. Find the equation of the tangent to y = 1-x² 3x+7 at the point where x = 1.

A:

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = V3x – 5

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 3) Let x = t2 - 1 , and y = e2 . Find the tangent line to the point (0, 1) .

A:

Q: 2х — What is the slope of the tangent line that touches the graph of In(y) +e-'=3y – 4x at the…

A:

Q: What is the slope of the tangent line that touches the graph of In y + e2"- = 3y – 4r at the point…

A:

Q: Finding derivative.

A: Given,

Q: Find an equation of the tangent line to the graph of  y = e−x^2 at the point (4, 1/e16).

A: Slope of tangent line is equal to value of the first derivative of y at given point.

Q: 3. Find the equation of the tangent line at point P(2,1) to the graph of the curve f(x) = v3x – 5

A:

Q: 12) Find the equation of the line tangent to g(x) = (3x + 11)ex-4 at x = 4.

A: ddxuv=vddxu-uddxvv2

Q: 2. Find the equation of the tangent line to the graph of f(x) = 3x?e-1 - 1, at r = 1.

A:

Q: 4x Find the equation of the line tangent to y = e at x =- In 5.

A: Problem related to application of derivative

Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

A:

Q: 12. Find the equation of the tangent line to f (x) = x³ at the point P(1,1).

A:

Q: Find an equation of the tangent line to the graph of f(x) = 2 + e1−x at the point (1, 3).

A: We have to find equation of tangent line to the graph of function fx=2+e1-x at the point 1, 3. We…

Q: 2 2х + 2х +1 G(x) = Jsech(x) y e dy

A:

Q: The slope of the tangent line to the graph of y = e3 at x = In 2 is

A:

Q: Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.

A: The given function is y=t+sin t    for  0≤t≤2π. Sketch the graph of the above function as shown…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.