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Q: Express the given interval in set-builder notation and graph the interval on a number line : [-3, 1]

A: Given-  -3,1 To express-  The given interval in set-builder notation and graph the interval on a num...

Q: Simplify exponential expression. 8x20/2x4

A: The given expression 8x202x4   Exponent rule: xaxb=xa-b

Q: Parametric to polar equations Find an equation of the followingcurve in polar coordinates and descri...

A: Consider the given curves, x=(1+cost)costy=(1+cost)sint Square and add the above equations, x2+y2=(1...

Q: Evaluate and simplify y'. y = 2x Vx - 2x + 2

A: Given,          y=2xx2-2x+2

Q: d 18x 5. In(9x? – 8) : dx 9x2 – 8

A: Consider the following expression: ddxln9x2-8 Apply the chain rule: ddxln9x2-8=19x2-8×ddx9x2-8=19x2-...

Q: Find the derivative of the function h(x) = x2 arctan5x

A: The given function is h(x) = x2 arctan5x

Q: Find the average rate of change of the function:  f(x) = 6x from x1 = 0 to x2 = 4

A: fx=6x Now, f0=60=0 & f4=64=24

Q: Find the critical points of the following function. Assume a is a nonzero constant.

A:

Q: Q17

A: The volume of the hemispherical bowl is V=23πr3. dVdt=3π cm3/sec At height h cm, the volume V is V=π...

Q: Scalar multiples Find scalars a, b, and c such that ⟨2, 2, 2⟩ = a⟨1, 1, 0⟩ + b⟨0, 1, 1⟩ + c⟨1, 0, 1⟩...

A: Given equation - 2,2,2 = a1,1,0 + b0,1,1 + c1,0,1Relating x, y and z coordinates on left and right h...

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

A: The equation of the curves are y=x3, y=0,  x=1.

Q: From a point on level ground 125 feet from the base of a tower, the angle ofelevation is 57.2°. Appr...

A: let a represents the height of the tower. In the right triangle, we have a known angle, an unknown ...

Q: The area between the graph of f (x) = x4 and the x-axis over the interval [0, 1]

A: Given equation - f(x) = x4Given intervals = 0, 1Let's draw the curve for the function given -  x...

Q: Find the limit of each rational function (a) as x→∞x→∞ and (b) as x→−∞x→−∞ f(x)=2x+35x+7f(x)=2x+35x+...

A: Divide both numerator and denominator by x and take limit

Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w an...

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by v1=v·...

Q: Evaluate ∫(x + sec2(πx))dx

A: The integral given is , ∫x+sec2πx dx Expand the integral ,  ∫x+sec2πx dx=∫x dx+∫sec2πx dx Solving th...

Q: Solve the linear equation: 2x - 7 = 6 + x

A: 2x-7=6+x

Q: Compute the derivatives of the following functions

A: The given equation is y2x3 - 7x = y sin(x+y) f(x,y) = y2x3 - 7x - y. sin(x+y) 

Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the dire...

A:

Q: solve each exponential equation. leave your answer in exact form (no decimals) logx+log(x+3)=1

A:

Q: (7 + h) The limit lim h→0 is the derivative of some function f(x) evaluated at x = a. Find the funct...

A: We know that, f'x=limh→0fx+h-fxh At x=a, f'a=limh→0fa+h-fah We have given f'a=limh→07+h23-723h On co...

Q: Fill in the blank/s: A text message plan costs $4 per month plus $0.15 per text. The monthly cost, f...

A: The fixed cost for the text message plan per month is $4. The variable cost for each text is $0.15. ...

Q: Solve: 23x-8 = 16

A: Since we have to solve 23x-8=16 -(i) and to find the value of 'x'=?

Q: Find:

A: Apply the limits. limx→1x2+2x-3x-1=12+21-31-1=1+2-30=00   Applying the limits gives 00 form.

Q: graph the following. be sure to include the ordered pairs, including any existing x-intercepts (loga...

A:

Q: Match the function with its graph. (a) f(x) = x (c) f(x) = Vĩ (b) f(x) = x' (d) f(x) = |x| I II III ...

A: Functions and graphs

Q: (a) Show that is one-to-one.(b) Use Theorem 7 to find (f-1)'(a) .(c) Calculate  f-1 (x)and state the...

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If y...

Q: Find the average rate of change of f(x) = x2 from a. x1 = 0 to x2 = 1    b. x1 = 1 to x2 = 2   c. x1...

A: Average rate of change of a function is given as: Ax=fx2-fx1x2-x1 Given function is fx=x2. (a). Aver...

Q: Determine whether the given statement is true or false. If the statement is false, make the necessar...

A: Given: f7=5 and g4=7. We know that fogx=fgx. Therefore, fog4=fg4=f7=5 Therefore, fog4=5

Q: Find the inverse of the functions (a) f(x) = 2x+5 (b) f(x) = (3-2x)/4 (c) f(x) = x+3

A: We have to find the inverse of the functions 

Q: Solve by the method of your choice: A stock can go up, go down, or stay unchanged. How many possibil...

A:

Q: Please show me all steps

A: Given,          ∫cot5xdx

Q: Fill in the blank/s: The notation a34 refers to the element in the ________ row and ______ column of...

A: Fill in the blank/s:  The notation a34 refers to the element in the ________ row and ______ column o...

Q: Calculus Question

A: Consider the given graph. The x value is taken along the horizontal axis and the function value fx i...

Q: Evaluate the integral.

A: To evaluate: ∫221t3t2-1dt Let substitute u=t2-1 dudt=12t2-1·2tdudt=tt2-1dt=t2-1tdu Limit will also c...

Q: Find the general solution of the given differential equations. y′′′ − 6y′′ + 12y′ − 8y = 0

A: The given differential equation is  y′′′ − 6y′′ + 12y′ − 8y = 0

Q: Differentiate the function.

A: The function given is, y=xx-1 Differentiate the function,  Apply the product rule ,  ddxu·v=ddxu·v+u...

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.