Q3: Find an equation for the tangent line to the curve y = etan x at the point where x = 0

Q: "/2 cos* x dx /4 sinb x

A:

Q: 5. Find the derivative of y = In(cos v3x + 2 ), by using chain Rule.

A:

Q: Express the integral in terms of the variable u, but do not evaluate it. 7x/10 – x? d; u = 10 – x² N...

A:

Q: 11. Which model seems most appropriate for this scatter plot? a. linear b. quadratic c. exponential ...

A:

Q: 4. Find a polar equation for the curve represented by the Cartesian equation y = 3x. T = r cos 0, y ...

A:

Q: Let a = ci + j and b = 6i + 8j. Find c so that the angle between a and b is %3D %3D Round your answe...

A: Solution is written in below steps.

Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j. NOTE: Enter the exact answe...

A: The unit vector in the direction of u is defined by: {\displaystyle \mathbf {\hat {u}} ={\frac {\ma...

Q: 11. A gate in an irrigation canal is constructed in the form of a trapezoid 3 ft wide at the bottom,...

A:

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x2 + ...

A:   Intersection points:  x2 + y2 - 4ax = 0                                                          ...

Q: Find the antiderivative, G(t), of the function g(t) = (5n²t? – t*)v5n2 – t2.

A:

Q: 4. Find . d?y of the functions x = 1+ cost and y = 1– sin t. dx2

A: Differentiating given parametric equationswith respect to t,x=1+costdxdt=-sint ...(1)y=1-sintdydt=-c...

Q: Determine the set of points satisfying the condition described by Iz – 2i| + |z + 4i| express in the...

A:

Q: Evalnate. the. followin..deuble.integrals.by.conver.king.b.. polar.Cto.r.dinates. Gp xpx Sf- Ans.: A...

A:

Q: -In 2 e* dx 3 (e2x + 8e*+ 7)2

A:      ∫0ln2exe2x+8ex+732dxLet u=ex.=∫121u2+8u+732du=∫121u+42-932duLet v=u+4.=∫561v2-932dv=∫\arcsec53π...

Q: +00 (x + 7)" Consider the power series > 2" Vn² – 1 | n=2 1. Use Limit Comparison Test to show that ...

A:

Q: Compute the partial sums S3, S4, and Ss for the series and then find its sum. 1 n+ 3 n+4 n=1 (Use sy...

A:

Q: 3. If f(x) = cos(x), determine f(125) (-T). V2 (B) 2 (A) 0 (С) 1 (D) –1 1 (E)

A: we will use nth derivative formula of cosx .

Q: (y- 2xy +6x ) dx-(x – 2xy + 2) dy = 0

A:

Q: G(t), of the function g(t) = (2n?t? - t)V2n2 – t?. %3D

A:

Q: Let a=ci+j and b=3i+6j. Find c so that a and b are orthogonal.

A:

Q: A pole that is 74 feet long is leaning against a brick wall. The bottom of the pole is getting farth...

A: This question is related to rate of change, we will solve it using given information. 

Q: dy then dx sin x If y = 1+ cos x ||

A:

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A:

Q: Use the Root Test to determine if the series converges or diverges (-1)"2* (-1)"2ñ zuć en? (2n2 – 1)...

A: Given problem:-

Q: 3n (2х — 1)8 п4 + 1 n=1

A:

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

A: To find out the volume of the tetrahedron whose vertices are given.  

Q: G Coshx dg G Sahr teンdx Anri y Ceshx = c

A:

Q: Consider the power series rvn(5– 2x)" 2n + 1 Vn(5 – 2x)* n=1 a. Show that the series is conditionall...

A:

Q: T/2 Evaluate using Wallis' Formula: sin? x cos5 x dx

A:

Q: Consider the plane 9x + 3y + z = 27. (a) Write down the point at which the given plane intersects t...

A:

Q: Find the vector component of v = (4, – 1, 7) along b = (2, 3, –6) and the vector component of v orth...

A: This is a problem related to vector. Based on the general formula vector we will solve the question.

Q: dy If y = x* then dx

A: This question can be solved by applying the concept of logarithmic differentiation.

Q: -3x 8 f(x) = - 5x + 8 - Step 2 of 2: Evaluate f "(3), f "(10), and f "(-2), if they exist. If they d...

A: First I have written the quotient rule of derivative and use it for given function and easily get th...

Q: An oil tank is being drained for cleaning. After t minutes there are Vlitres of oil left in the tank...

A: Here we will find all asked quantities,  

Q: Is the series divergent, absolutely convergent, or conditionally convergent

A: This is a problem related to series and sum calculation. Based on the general formula we will determ...

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y? = 2(x2 – ...

A:

Q: tind the deatNe of 2メー3 うメース the definition - ensing

A:

Q: Let D be the smaller cap cut from a solid ball of radius 20 units by a plane 10 units from the cente...

A: Given sphere:  x2 + y2+z2 = 202                     sphere

Q: Average Rates of Change Use each graph to estimate the average rate of change of the percentage of n...

A: We need to find the average rate of change for the given graphs.  

Q: A torus is generated by rotating the circle x? + (y – R)2 = r² about the x-axis. Find the volume enc...

A: Given circle is x2+(y-R)2=r2 Here the torus is generated by rotating the circle about x-axis. Find t...

Q: Consider the two functions fz) = 5x +5 and g(x) = 5x² - 5. a. Determine the instantaneous rate of ch...

A: rate of change means differentiate with respect to x so differentiate it f'(x) = 10x g'(x) = 10x   a...

Q: Find the volume of the solid generated of the area in the first quadrant bounded by y = 3x – x3, x =...

A:

Q: 2 2 cos 0 d0 V1 – sin 0

A: Given:        ∫0π2cosθ1-sinθdθ substitute u=1-sinθ→dudθ=-cosθ→dθ=-1cosθdθ      =∫10-1udu       =-∫01...

Q: Find the area bounded by y = sin(x) and y = sin*(x) from 0 < x <.

A:

Q: 2 A spherical snowball is being made so that its volume is increasing at the rate of 8ft³ jmin/ Find...

A: This is a problem related to the volume of the spherical snow ball and change in rate. By using conc...

Q: Find for the given function. w= 10z2 e?

A:

Q: Find the derivative of the follo solutions. 1. What is (5x +3)4? dx 2. What is 4 (x2 – 3x)5? dx 3. W...

A:

Q: Original Integral Rewrite Integrate Simplify dx 9. X + C dx

A:

Q: cos (x² + y') = x - lg Find dy using implicit differentiation: 2. %3D dx

A:

Q: Consider the parallelepiped with adjacent edges u = 6i + 6j + k v = i+j+7k w = i+ 4j + 3k Find the v...

A: