* Question Completion Status: Moving to another question will save this Question 9 Integrate the function. dx ,x > 7 -49 x2-49 + C In 343 + C O Inx+V2 - 49 | + C + C 49x

Q: The formulas gives combinations of three vectors a, b, c. For each, decide if the product is defined...

A: a) is not defined as (b.c) is scalar. b) is defined if we bracket a×b c) is not defined because of b...

Q: What are the Average rates and secant line?

A: Assume we have a function f(x) The Average Rate of Change of function f(x) on the interval [a, b] is...

Q: Computing directional derivatives with the gradient Compute the directional derivative of the follow...

A: given: g(x,y)=ln4+x2+y2

Q: Evaluate the following integrals.

A: Given: I=∫sin4x2dx we know that 1-cosθ2=sin2θ2 so, putting  sin2x2=1-cosx2

Q: Use words to describe the given formula, cos * cos * = (1/2) [cos(*- *) + cos(* + *)]

A: We know that cos(A+B)=cosAcosB - sinAsinB           ...(1) cos(A-B)= cosAcosB + sinAsinB          .....

Q: Consider the functions w = f(x, y, z) = xy²+zy and x (t) = cos t, y (t) = sin t with z (t) = tan t. ...

A: w(x,y,z)=xy2+zy and x(t)=cost,  y(t)=sint  with   z(t)=tant

Q: The number of banks in the country for selected years from 1980 to 2009 is given by y =-375.7 x +18,...

A:

Q: Evaluate the integral. |cos 7x cos 3x dx

A: The given integral ∫cos7xcos3xdx.

Q: A 50ft ladder is placed against a building. The base of the ladder begins to slip away from the buil...

A: Let us denote x=horizontal distance from the wall  y= vertical distance from the base  Given that dx...

Q: Use the given measurements to solve the the given triangle with a = 300, b = 200. Round lengths of s...

A:

Q: For the following matrix which of the list of vectors are eigenvectors and what are there associated...

A: For the given matrix and the set of vectors we have to determine which of them are eigenvectors of t...

Q: The graph shows the areas of regions bounded by the graph of ƒ and the x-axis. Evaluate the followin...

A:

Q: Determine if the functions are even odd or niether

A: A function is said to be odd function if, f(-x)=-f(x) A function is said to be even function if, f(-...

Q: The formulas gives combinations of three vectors a, b, c. For each, decide if the product is defined...

A: given: the three vectors a ,b and c  

Q: express the integrand as a sum of partial fractionsand evaluate the integrals. ∫ y2 + 2y + 1/(y2 + 1...

A: To express the integrand as a sum of partial fractions and evaluate the integral. ∫y2+2y+1y2+12dy  

Q: At what points on the curve x=3t^2 + 1, y=t^3 -1 does the ranger line have a slope 1/2?

A: The slope of the tangent line is given by, dydx=dydtdxdt=ddt3t2+1ddtt3-1=6t3t2=2t Given that the slo...

Q: You are choosing between two texting plans. Plan A has a monthly fee of $15 with a charge of $0.05 p...

A: Given: Monthly fee of plan A is $15 with a charge of $0.05 per text. Monthly fee of plan B is $5 wit...

Q: Calculus Question

A:

Q: Determine whether the integral is convergent or divergent. -1 e-37t dt If it is convergent, evaluate...

A: Given: The integral ∫-∞-1e-37tdt. To discuss: About the convergence and divergence of given improper...

Q: Find the integral of r(t) = (3t2 + 4t, 2, e') from 0 to 1.

A: Consider the following vector: rt=3t2+4ti^+2j^+etk^ Integrate the above vector: ∫013t2+4ti^+2j^+etk^...

Q: express the numbers in terms of natural logarithms. cosh-1 (5/3)

A: We have given cosh-153 Let x=cosh-153 ⇒coshx=53 We know that coshx=12ex+e-x Therefore, 12ex+e-x=533e...

Q: Begin by graphing the standard quadratic function, f(x) = x2. Then use transformations of this graph...

A:

Q: Q8- Find an equation for the tangent to the curve at the given point. Then sketch the curve and tang...

A:

Q: 1. Find the derivative if f(x)= ((x/2) + (x √x))ex

A: The given function is fx=x2+xxex. Obtain the derivative as follows.  

Q: if x 2 (a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.) ...

A: a) limx→1-g(x)=limx→1-(x)=1limx→1+g(x)=limx→1+(2-x2)=2-12=1So, limx→1-g(x)=limx→1+(x)=limx→1(x)=1 g(...

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. dx

A: Given  ∫017x5dx The given function is not continuous at x=0.so to check the whether the integral is ...

Q: Calculate the work in megajoules (1 MJ = 1 × 10° J) required to pump all the water out of a full tro...

A: Given: To calculate work required by pump from a trapezoidal prism shaped trough with dimensions Bot...

Q: Sketch the region bounded by the graphs of the equations g(x) = 4 / (2 − x),     y = 4, x = 0and fin...

A:

Q: If lim f(r) = lim g(x). then whether f(x) = g(x) is always true ? Justify D←エ your answer by an exam...

A:  If limx→af(x)=limx→ag(x),then we have to determine whether f(x) always equals g(x).

Q: Break-Even Analysis: School Construction Costs The cost, in millions of dollars, of building a three...

A: Given data:   The expression for the cost of building school is C(x)=1.7+0.14x-0.0001x2. The given t...

Q: x+y – 2z = 1 5y + 2z = 3 -2x – y + 3z = 2 By Cramer's rule, solve the system

A: We first make the coefficient matrix and find its determinant.  11-2052-2-13=1(15+2)-1(0+4)+(-2)(0+1...

Q: Use the quotient rule to show that the derivative of csc(x) is − csc(x) cot(x). That is, prove that ...

A: Given: h(x)=cosec x  By using the quotient rule we have to show that ddx(cosec x)=-(cosec x).(cotx)

Q: Determine the domain and range of y

A: The given function is y=16-x2x-2   ......(1)

Q: 07// Evaluate limy→o sin3y cot 5y y cot 4y

A:

Q: Calculus Question

A: Since you have solved #a-c, I'll show #d-f d) On the extreme right side of the graph y is approachin...

Q: Finding a second derivative. Find d^2y/dx^2 implicity in terms of x and y

A:

Q: Add or subtract as indicated and write the result in standard form: (7 + 2i) + (1 - 4i)

A:

Q: F(-5)=F(-3)=F(-2)=F(π+)=

A: According to company policy we are allowed to provide solution for only first 3 sub parts. If you re...

Q: Express the following sums using sigma notation.(Answers are not unique.)a. 1 + 2 + 3 + 4 + 5b. 4 + ...

A: Consider the first expression: 1+2+3+4+5=∑n=15n Consider the second expression: 4+5+6+7+8+9=∑n=49n

Q: Solve the initial value problem y = 8x*e=2w, y(1) = 0..

A:

Q: Investigate the behavior of the function as n or x grows large by making a table of function values ...

A:

Q: Determine the open intervals on which the graph is concave upward or concave downward. (x2+4)/(x2-1)

A: Given: fx=(x2+4)(x2-1)

Q: End behavior Evaluate lim flx2 and lim f1x2. 4x3 + 1 f1x2 1 - x .3

A: the given function is: f(x)=4x3+11-x3

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.